There is provided a vehicle power steering system. In the vehicle power steering system, a first assist torque component (Ta1) is computed based on a steering torque (Th) and a vehicle speed (V). A target steered angle ([theta]p*) is computed based on the first assist torque component (Ta1) and the steering torque (Th), and a second assist torque component (Ta2) is set based on the target steered angle ([theta]p*) and an actual steered angle ([theta]p). Then, the vehicle power steering system assists a steering operation by applying an assist torque Tas corresponding to the first assist torque component (Ta1) and the second assist torque component (Ta2) from an electric motor to a steering shaft. Further, an ideal steered angle at which a vehicle is able to keep travelling in a lane is set based on image information on the lane, which is captured by a camera, and a correction value ([delta theta]p*) is computed based on the deviation between the ideal steered angle and the actual steered angle ([theta]p). Then, the target steered angle ([theta]p*) is corrected by the correction value ([delta theta]p*).