Houston police said a man was riding his bicycle southbound on Almeda and went into the right lane in front of a car.
According to investigators, the driver of the car did not see the cyclist until the last second.
Officials said the man tried to stop his car, but he struck the bicycle.
The bicycle and its rider went over the top of the car.
The cyclist was transported to Ben Taub General Hospital in serious but stable condition.
The driver of the car was not injured and waited for police to arrive at the scene.
Officials said no charges are expected because it appears to be the cyclist's fault.