Space Runaway Ideon begins in 2300, far enough in the future that mankind has begun colonizing other planets. On the planet Solo in the Andromeda Galaxy, a group of archaeologists had come across the mysterious remains of the Ideon—three large armored trucks with the ability to transform into a godlike mecha. They also come across a large spaceship. For six months they had diligently restored the machines but failed to get the giant tanks to move. Suddenly, a humanoid alien civilization known as the Buff Clan comes across Solo.
Karala, the daughter of the Buff Clan's military commander flies down to the planet against orders to investigate (her commanding officer, Gije, is reluctant with her, due to her standing and the fact that he once was a soldier under her father). She is pursued closely by comrades sent by Gije, but they lose sight of her. Assuming the "aliens" (Earthling colonists) have attacked Karala, the Buff Clan begins to attack. Cosmo Yuki, the afro-wearing protagonist of the series, climbs aboard one of the three tanks and, when it initially forms the Ideon, fends off the first assault, repelling Gije's men.
This is a short respite, though, as another force is sent down soon after. Bes Jordan, leader of the sparse military force stationed with the colonists orders that the Ideon tanks be armed with missiles, but while that's happening the cities on Solo are obliterated by the Buff Clan soldiers. An air raid siren is sounded and the survivors, using the Ideon for protection, board the spaceship found with the Ideon (known as the "Solo Ship") and flee. The survivors travel from planet to planet, constantly pursued by the Buff Clan who desire the Ideon for themselves along with the mysterious energy source behind them, known only as the "Ide".
The Ideon is piloted by several Solo Ship crew members, but the main pilot is Cosmo Yuki.
As the crew of the Solo Ship fight and survive further, the true power of the Ideon begins to slowly be revealed with terrifying results. Although the crew often latches onto various hopes and optimism, as the death toll of the crew rises and the devastation surrounding them increases, the crew of the Solo Ship slowly begin to despair. Eventually turned away by their own world out of fear, what fate awaits this lost ship and its inhabitants?