To reduce burden on a driver even if travel resistance gets larger, and to prevent abrupt output of auxiliary driving force even if the traveling vehicle collides with a stepped structure.

The vehicle with auxiliary driving force device comprises: an acceleration calculating means 12 calculating acceleration of the vehicle; a torque sensor 13 measuring man-power driving force with respect to the vehicle; a motor 11 giving the auxiliary driving force; an auxiliary driving force measuring means 14 measuring the auxiliary driving force; a travel resistance calculating means 16 calculating the travel resistance acting on the traveling vehicle based on data about the acceleration, man-power driving force, and auxiliary driving force acquired from each means; a means 17 for calculating the auxiliary driving force by the resistance corresponding to the travel resistance; a motor output calculating part 18 of the auxiliary driving force calculating means, for calculating the auxiliary driving force based on the auxiliary driving force by the resistance; and a delaying means 19 delaying change in output of the auxiliary driving force.