A vision system for a vehicle includes a forward-viewing camera located behind and viewing through a vehicle windshield, a rear camera located at a 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. The common image processor utilizes object detection software at least during processing of first image data captured by the forward-viewing camera to detect at least one vehicle present exterior the equipped 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 camera are displayed on the video display screen.