This game takes place in the Lylat system, a stellar system in the fictional Star Fox universe that is inhabited by anthropomorphic animal races (i.e. foxes, frogs, dogs, birds, rabbits, apes, etc). It contains the planets Corneria and Venom, both representing good and evil, respectively. One can visit many other planets, asteroid belts, space stations, etc. while going through the course of the game. Whichever path the player chooses affects what places they will encounter.

Star Fox is an elite mercenary unit hired by General Pepper to defeat Andross. Fox McCloud is the leader of the team, and he is accompanied by his teammates Falco Lombardi, Peppy Hare, and Slippy Toad. The player controls Fox, while Falco, Peppy and Slippy occasionally come to his aid or need his help.

The evil Andross has launched an attack against Corneria and the rest of the planets in the Lylat system, and it is up to Star Fox, an elite mercenary team led by Fox McCloud, to stop him. The battle begins on Corneria and proceeds through the system, eventually arriving at the planet Venom, location of Andross' headquarters, and culminating in a one-on-one battle against Andross himself.