A collision avoidance support apparatus sets a side area right beside an own vehicle in an adjacent lane as a constant-speed target space, which is used for lane change at a constant speed, and also sets a diagonally-front area and a diagonally-rear area as alt-speed target spaces, which are used for lane change at an accelerated speed and at a decelerated speed. Then, a target space that is free of other vehicles is extracted by the apparatus. If there is no target space that is free of the other vehicles, the lane change is determined as unsafe. If there is no other vehicle in the constant-speed target space, the lane change is determined to be safe at the constant speed. If there is no other vehicle in at least one of the alt-speed target spaces, the lane change is determined to be safe at an accelerated speed or a decelerated speed.