A vision system for a vehicle includes a forward-viewing camera located behind and viewing through the vehicle windshield, a rear backup camera located at the rear of the vehicle, and a common image processor operable for processing captured image data. A video display screen is located within the interior cabin of the vehicle viewable by a driver of the vehicle. Responsive to the vehicle being shifted into a reverse gear and while the driver is executing a reversing maneuver, video images derived from image data captured by at least the rear backup camera are displayed on the video display screen. When the vehicle is travelling forward, the common image processor processes image data captured by the forward-viewing camera for a lane departure warning system of the vehicle and for a headlamp control system of the vehicle and/or a traffic sign recognition system of the vehicle.