The year is 2220, 21 years after the first Yamato made its way to Iscandar and 17 years after the destruction of the Yamato in "Final Yamato". A wandering, cascade black hole is approaching the Solar system, and will soon reach the Earth destroying it and everyone on it. A decision is made that for humanity to survive they must evacuate the entire population.
However, there is only 90 days before the black hole reaches earth and to complicate matters there are alien governments working together in an effort to stop the Earthlings from leaving as they are deamed to be invaders. The Yamato must again be entered back into service to overcome these obstacles and save the people on Earth.