A surveillance picture shows the man wearing a hat and glasses. Police said he may have left from a back parking lot and then headed north.
So far, police said he hasn't been caught.
Police said the man walked into the bank with a note demanding money, wearing a black hat, silver glasses and a collared shirt with a Hilton Head logo on it.
Police said he implied he had a gun, but never pulled a weapon on the teller.
Investigators said the robber is between 5 feet 7 inches and 6 feet with a thin build.
Police haven't said if he was in a car.
No one was injured during the robbery.