A driving power source rotational speed control device is provided in a vehicle outputs power of a rotary driving power source via a continuously variable transmission as motive power, that changes the rotational speed of the rotary driving power source in association with changes in the vehicle speed when acceleration is requested. The control device includes: acceleration/deceleration state determination means determines whether the vehicle is accelerating or decelerating when acceleration is requested; and rotary driving power source rotational speed change setting means sets the change gradient of the rotary driving power source rotational speed to establish the association of the rotary driving power source rotational speed with changes in the vehicle speed when acceleration is requested. The rotary driving power source rotational speed change setting means suppresses reductions in the rotary driving power source rotational speed when the acceleration/deceleration state determination means determines that the vehicle is decelerating.