A driving force controlling apparatus includes a driving force controller configured to determine a state of a road surface. A driving force controller is configured to control a driving force of a vehicle based on the road surface state. A rear-wheel speed sensor is configured to detect a rear-wheel speed. A low-friction-coefficient road surface determining device is configured to determine whether the road surface is a low-friction-coefficient road surface using the rear-wheel speed on a predetermined condition. A determination prohibition device is configured to prohibit the low-friction-coefficient road surface determining device from determining whether the road surface is a low-friction-coefficient road surface, if (a) the rear-wheel speed sensor is abnormal, or if (b) a predetermined time has elapsed from when a shift range is changed from a reverse range to a drive range and/or (c) a gear position has become greater than or equal to a predetermined gear position.