In a driving support device for a vehicle, a collision prediction unit uses a determination plane defined by a lateral position axis indicating a position with respect to a vehicle in a lateral direction orthogonal to a vehicle traveling direction and a prediction time period axis indicating a time-to-collision set in the vehicle traveling direction. The collision prediction unit establishes a collision prediction area as an area in the determination plane. Further, the collision prediction unit determines whether at least a part of the section between both ends of a target is within the collision prediction area in the determination plane. Depending on the determination, the collision prediction unit predicts a collision with the target. The width of the collision prediction area along a lateral position axis is set based on the width of the vehicle. The lateral position of the collision prediction area is set based on a product between the speed of the target and the time-to-collision.