Mayor Thompson says the suspect put a gun to his head as he exited his vehicle. The suspect then demanded cash. The mayor complied. He also gave the man his telephone.
The suspect threatened to kill him and Thompson says he thought he could be shot.
"Telling me he was going to shoot me if I kept turning around an looking at him," Thompson said. "So he ordered me to climb underneath the car. I went around to the back of the car and I slid underneath the car. I heard him running away."
The suspect fled on foot. The mayor says the police department will do everything it can to find the suspect.
Officials think the suspect could be the same man who attacked another Sugar Land homeowner in his driveway earlier this week. That suspect has been described as a tall thin African American man in his early 20s.
The mayor tells Eyewitness News he doesn't normally carry a gun, but that's something he now may reconsider. Thompson is a veteran of the US Air Force. Thompson believes this was a random act, and that he wasn't targeted because of his position as mayor.
Crime Stoppers has offered a reward of up to $5,000 for information leading to the arrest and conviction in this case.
Harris County Sheriff Adrian Garcia also knows how it feels to become a victim of crime. Last month, he walked outside his home to find that someone had stolen the wheels off his SUV. So far, police have not made any arrests in that case.