In the very near future, a race of huge, insectoid aliens are discovered traveling the galaxy. These aliens, which are known as the Uchuu Kaijuu, or Space Monsters (Note: This name is what they are referred to throughout the series, although the Super Robot Wars games names them the "STMC" or "Space Terrible Monster Crowd"), seem dedicated to the eradication of the human species as the latter takes its first steps away from the solar system, and they are getting closer and closer to Earth. Humanity has responded by developing space-going battleships and giant fighting robots. These complex robots—RX-7 Machine Weapons—are actually an advanced type of fighting suit, piloted by a single occupant. As advanced as they are, however, they are being used as trainers for a new weapon, the Gunbuster. However, being relatively new technology, they are difficult to operate (stock shots show pilots working multiple controls with hands and feet, while fingers rapidly operate switches on the hand grips), so pilot candidates are selected from the best and brightest youth on Earth and the Lunar colony. These are trained at schools around the world.

The story begins in the year 2023, six years after the first battles with the aliens (the actual battle started in the year 2015 however due to time dilation, two years went by on Earth by the end of the battle), and centers on young Noriko Takaya (タカヤ・ノリコ Takaya Noriko) (voice: Noriko Hidaka). Although Noriko's father was a famous admiral in the space fleet who went missing following one of the first battles of the war, her own talents as a pilot are questionable—especially when compared to the other students. Nonetheless, she has entered a training school on Okinawa, where she is largely influenced by her instructor, Kouichirou Ohta ("Coach Ohta"), who was one of Admiral Takaya's crew. He has faith that she will overcome her early clumsiness, while other students are critical of her inability.

Noriko idolizes the beautiful, competent and talented Kazumi Amano (アマノ・カズミ Amano Kazumi) (voice: Rei Sakuma). She is not alone, the other students recognize that Amano is the top RX-7 pilot at the school, and likely the entire world. Coach Ohta shows the extra training which Amano creates for herself, inspiring Noriko to look within herself for strengths which she did not know that she had.

Only two Gunbuster pilots from each school will be selected for the real mission. Amano, of course, will be going, and all of the others want the second slot on the team. Takaya is determined to win, not only to be with Amano but also to find (or avenge) her father. She is thrilled to discover that she has in fact been chosen as the second Japanese pilot.

Following that selection, conflict between Takaya and other students comes to a head, when the second-best RX-7 pilot at the school publicly challenges her to a one-on-one fight. Planned for late at night, when none of the school authorities will be around to stop it, Ohta learns of the duel and comes to the battleground—but does nothing. He is there to observe, and perhaps to save Takaya's life, if the combat gets too intensive.

Takaya is on the defensive from the start, and the older student humiliates her by action and over the radio. As Takaya's RX-7 is pummeled, Noriko realizes that her difficulties are a case of sensory overload—she is getting too much information from the electronic monitoring systems. She turns off her monitors, but as the systems go dark, her opponent is infuriated by the perceived insult and prepares the final, killing blow. Just as it appears that Noriko is doomed, she destroys her opponent's RX-7 with a "Thunder Kick". Her opponent muses that the school rookie has beat her with an advanced maneuver which she hadn't been taught. This is the proof that Ohta was seeking, that Noriko had an innate ability which would be invaluable in the battles to come.

Together, with Coach Ohta and Amano, Takaya is sent into space to train with other representatives from all over the solar system in preparation for the attack upon the space monsters. There they are introduced to a soviet pilot from the moon base by the name of Jung Freud. On their first training mission, Takaya and Amano are stopped by Jung, and challenged to a duel. Amano and Jung become completely involved in the fight, as Noriko trails along, and all three get lost within the machinery of the space station. The fight stops midway, when all three come in contact with the first space monster that was defeated and captured.

Once they return they are scolded by their coach, but because of their importance to the missions success as well as building feelings between the coach and them, they are let go with a simple warning. Jung later apologizes for her challenge, and thus begins a friendship with the two.

As they move farther into space, the young pilots are placed in their quarters for subspace traveling. On a dare, Takaya is sent into the hangars and meets a male space pilot named Toren Smith. Amano comes into doubt of Takaya's abilities and asks the Coach to end their partnership. Takaya overhears the conversation and ends up partnering with Smith instead.

The first true battle between the aliens begin, and the humans realize how vastly outmaneuvered and outnumbered they are. They are able to retreat with limited casualties, but Takaya has lost Smith, and gained an uncontrollable fear towards deep space combat. As their second battle approaches, Takaya is determined to improve and asks the Coach for private lessons. Jung finds out and thinking that she doing so to control Gunbuster, challenges her in space. But even before they are able to fight, Takaya breaks down within her suit and is taken to the infirmary.

The captain decides to retreat to Earth, but the fleet is attacked in sub-space, leading to the destruction of the majority of their forces. Once they reach Earth's orbit, only the Exelion and a few minor cruisers are still active. Though their struggle appears bleak, Takaya manages to summon up her strength for the sake of her friends and crew members. She takes control of the incomplete Gunbuster and uses its high-powered weaponry to force the enemy to retreat. The battle is over, but those who remain are faced with the harsh reality of war and its aftermath.

Afterwards, the three pilots return to Earth, where things have changed significantly. Due to the effects of time dilation, 10 years of relative time has passed on Earth while the pilots were in space. Takaya's former nemesis who had previously challenged her at school is now the coach for new pilots. Her best friend, Kimiko, is now a mother with a 3 year old daughter, and Earth has been working on a 70 km long space ship as a form of defense in the event of a space monster attack.

While in a peaceful lull, Takaya and friends try to re-adjust to living in a world that has already passed them by. Takaya tries to reconnect with her friend, while Amano tries to share her feelings with the Coach. The peace is broken, however, when Earth is notified that a space monster fleet of unprecedented size is headed towards Earth. After many arguments, the idea of sending the old Exelion as an unmanned black hole bomb, is proposed. The Gunbuster is nominated to escort the bomb there, and then to come home.

Takaya and Amano, in separate ships which combine into Gunbuster, are sent out, a trip that will last an hour or more to them, but half a year to everyone back on Earth. As they almost reach their goal, Amano breaks down, admitting that she does not want go forward, since each second forward means the longer she is away from their Coach, who is now dying from space radiation. Takaya is able to convince her to continue, and their mission is a success. Upon returning, they are relieved to learn that the Coach is still alive; he and Amano then get married.

The final episode takes place 15 years later. Amano has lived on Earth during this time, but after the Coach passes away, she decides to take on a final mission. The space monsters have resurfaced, and in retaliation Earth has been building small planet-sized black hole bomb, which has been created using the mass of Jupiter pressured into the size of the moon, known as Buster Machine III. When detonated, the bomb and 3,000 'slave mines' placed around the center of the galaxy, will cause a black hole to be formed thereby sucking in and destroying the space monsters.

Amano is sent back into space to board the new ship Eltrion, where mobile suits called Sizzlers (buster sized machines, piloted individually) are now used in combat. With the crew present to welcome Amano, she and Takaya share an emotional reunion, though the absence has felt much longer for the former. Takaya has difficulty coming to terms with the fact that so much time has passed on Earth, after only 6 months relative to her.

When the final battle begins, Amano is ordered to man the Gunbuster with Takaya, and both fight alongside others to defend the bomb. The alien army is fended off, allowing the black hole bomb to be set. However, when the time comes to activate, they find out the enemies' attacks have damaged 2% of the 'slave generators' required for implosion. Amano and Takaya decide to dive down into the core of Buster Machine III and activate it by using one of Gunbuster's two Degeneracy reactors, even though doing so means they will likely be unable to leave without suffering severe relativistic time dilation during their escape.

After the bomb is set off, Noriko and Kazumi spend 12,000 Earth years objective traveling home, although for them only hours or days have passed. Upon arriving in Earth orbit in the damaged Gunbuster, the pilots cannot make contact with anyone nor see any sign of habitation on the planet, suggesting that human civilization is long gone. However, their despair is instantly dispelled when a massive light pattern suddenly appears on the planet saying "WELCOME HOME!" spelled out in simplified Japanese (the final letter, however, is reversed, which indicates the current civilization was mimicking the bygone language). Delighted that their planet is alive and well, the pilots bid the Gunbuster farewell and return to Earth.