DRIVE ASSIST DEVICE

The control unit for controlling the travel control device causes the host vehicle to decelerate and stop at a predetermined position in front of the host vehicle when a stop target is detected in front of the host vehicle, and further. The control unit estimates a time period from when the subject vehicle catches up with the pedestrian until when the subject vehicle stops and a time period from when the subject vehicle stops until when the pedestrian catches up with the subject vehicle when the subject vehicle is less than the reference value when the sum of the two times is less than the reference value, maintains the subject vehicle in the stop state even if the subject vehicle is not detected.