A vehicle collision avoidance assist apparatus executes a steering avoidance control of setting an avoidance route for avoiding the collision of the own vehicle with the object in a lane in which the own vehicle moves and executing an avoiding steering process of forcibly steering the own vehicle so as to move the own vehicle along the avoidance route when an index value representing a probability of collision of an own vehicle with an object ahead of the own vehicle becomes equal to or greater than a predetermined index value. The apparatus stops an execution of the steering avoidance control when a departing amount of the own vehicle from the avoidance route becomes equal to or greater than a predetermined departing amount while the electronic control unit executes the steering avoidance control. The predetermined departing amount is set for each of sections of the avoidance route.