A system for controlling steering of a vehicle, including an electric motor used for power-steering torque assist control. In the system, the lane-keeping-steering assist torque TLK for causing the vehicle to run along the center of a road existing ahead of the vehicle is calculated, while the power-steering assist torque TPS for assisting the vehicle driver's steering is calculated. Then, ratios RTO
are calculated based on the detected steering torque. The assist torques TLK, TPS are corrected by multiplication with the ratios RTO
respectively and are added together to determine a final assist torque TA, and based on the final assist torques TA, a motor current to be supplied to the electric motor is determined, thereby enabling to effectively prevent the two kinds of control from interfering with each other so as not to adversely affect the vehicle driver's perception of vehicle steering response. Additional ratios are determined based on the detected steering torque change and the vehicle speed.