A vision system for a vehicle includes a rear backup camera and a display device including a video display screen. Within two seconds of shifting the vehicle transmission into reverse gear, the display device displays rear backup video images derived from captured image data. Rear backup video images derived from captured image data can be displayed after shifting out of reverse gear until a threshold condition is met. A user input is actuatable by the driver of the vehicle to change display of rear backup video images to display of other video images. Display of the other video images occurs after a delay period has elapsed since shifting into reverse gear. During the delay period and commencing when the vehicle transmission was shifted into reverse gear, only rear backup video images derived from image data captured by the rear backup camera are displayed by the video display screen.