A steering assist system for applying a steering torque reduces the influence of a time-dependent steering control amount on an assist steering torque when a predetermined driving operation by a driver is detected. Thus, the influence of the time-dependent steering control amount on the applied steering torque, which increases when the period of time over which actual moving state deviates from the target moving state increases is reduced when the driver makes the predetermined driving operation. Thus, it is possible to avoid the problem where steering feel degrades because the steering torque increases over time.