A vehicle collision avoidance assist apparatus is capable of alerting the driver of a host vehicle that is to enter an intersection to the probability of collision or the like at right timing in order to prevent a crossing accident using information acquired from remote vehicles through inter-vehicle communication. The attention of the driver of the host vehicle to the front side including the intersection is increased when a large number of remote vehicles exist around the intersection which the host vehicle is to enter, compared with a case in which the number of remote vehicles around the intersection is small. The vehicle collision avoidance assist apparatus makes the alert, such as a warning, later than reference alert timing (normal alert timing) in consideration of the above situation to suppress excessive alert.