Terrifying footage shows Britton Hayes sitting perfectly still with a look of silent terror on his face as the beast perches on the seat behind him.
Hayes, who can be seen in the video, said that the group was watching three cheetahs when one of the big cats spotted the vehicle and hopped onto the bonnet.
They were busy watching the animal as a second one decided to hop into the back, News.com.au reported.
"While we were all watching the cheetah in the front, one of the brothers had flanked around the back and hopped in back of the vehicle to try and sniff us and make sure that we weren't a threat," Mr Hayes told Komo News.
The group's guide told them all to avoid eye contact with the animal and stay calm.
On the video, which was taken by Peter Heistein, the cheetah can be seen sniffing the inside of the car and clawing and nibbling at the head rest of an empty seat.
Mr Hayes said he tried to slow his breathing so the animal wouldn't sense his fear.