Women (81 percent) are more likely than men (67 percent) to be afraid to allow an autonomous vehicle to drive itself with them in it.
Baby Boomers are more fearful of self-driving cars than younger generations, the study found.
Ironically, AAA said the demand for semi-autonomous vehicle technology is high.
Nearly 61 percent of American drivers say they want such technology on their next vehicle.
The technology is considered to be the "building blocks" for self-driving cars. It includes automatic emergency braking, adaptive cruise control, self-parking technology and lane-keeping assist.
"With one-in-five Americans planning to purchase or lease a vehicle this year, AAA urges car shoppers to fully understand today's advanced vehicle technology, particularly the limitations, before purchasing a new car," it said.
Drivers who have semi-autonomous features on their vehicles are 75 percent more likely to trust the technology than those who do not have it.
This suggests "that gradual experience with these advanced features can ease consumer fears," AAA noted.
The study follows a recent announcement by Google that one of its self-driving cars sideswiped a bus in February on a road in California. There were no injuries.
Edmunds says: Familiarity with self-driving vehicle technology will lead to trust, this study suggests.