Rainsford was on his way to Rio de Janeiro, Brazil to hunt jaguar. That was the plan, until he fell off his yacht. He washed up on a nearby island, called Ship-Trap Island by the locals.
He explores the island until he comes across a fortress. He is greeted by a large Cossack named Ivan, and Ivan is a servant to another Cossack named General Zaroff, who is an avid hunter.
Zaroff and Rainsford share a meal, where Zaroff reveals that he is an experienced big game hunter, to the point where he is bored with all the prey he hunts, except one. It turns out that Zaroff likes to hunt people for sport, and he wants to hunt Rainsford.
The hunt for Rainsford begins, and Rainsford runs off and sets traps that end up killing Ivan and Zaroff's most prized dog, but not Zaroff. Zaroff is more and more amused with each trap.
At the end of the day, Rainsford is backed up into a corner, with no way out but down into the ocean, so he jumps. Zaroff decides to retreat for the day.
After Zaroff gets home, eats dinner, and gets ready to go to bed, Rainsford ends up ambushing Zaroff in his own bedroom. The two end up dueling, and Rainsford wins.