With a power steering system and a control method of a power steering system provided, a basic assist control amount is calculated based on a steered state of a driver's steering wheel. A compensation control amount used to compensate for the basic assist control amount is calculated, and corrected, during calculation of the compensation control amount, based on a lane-position maintenance assist control amount which is calculated based on a running state of a vehicle and which is used to maintain a predetermined lane-position. A target assist control amount applied to a steering mechanism is calculated based on the basic assist control amount, the lane-position maintenance assist control amount, and the compensation control amount.