A collision avoidance system for use in a vehicle includes a forward-viewing camera and a rearward-viewing camera. Responsive to image processing of captured image data, the system detects the presence of vehicles present ahead of the equipped vehicle and in the traffic lane the equipped vehicle is driving in and in an adjacent traffic lane that is adjacent to the traffic lane the equipped vehicle is driving in. Responsive to image processing of image data captured by the rearward-viewing camera, the system determines imminence of a rear impact with the equipped vehicle by another vehicle and the system controls a steering system to move the equipped vehicle to the adjacent traffic lane provided the portion of that adjacent lane the equipped vehicle is to move to is unoccupied by a vehicle ahead of, adjacent to or behind the equipped vehicle.
