When a host vehicle is likely to collide with an object ahead, a vehicle collision-avoidance assist device sets a target avoidance path by which the collision is avoidable, and executes avoidance steering of forcibly steering the host vehicle so as to travel along the target avoidance path upon an avoidance steering starting condition being met. When another vehicle traveling next to the host vehicle is a vehicle traveling alongside, the device stores a vehicle-traveling-alongside travel region, and when the other vehicle is an oncoming vehicle, the device stores an oncoming vehicle travel region, and acquires a travel region of the host vehicle along the target avoidance path as an avoidance travel region. The device does not execute the avoidance steering when the avoidance travel region overlaps with the oncoming vehicle travel region, but executes the avoidance steering when the avoidance travel region overlaps with the vehicle-traveling-alongside travel region.