An automatic steering system comprises a controller. The controller executes target steering angle calculation processing. The controller further calculates a learning value of lateral acceleration. The learning value is calculated based on an error of a detected value of the lateral acceleration by an acceleration sensor and an estimation value of the lateral acceleration calculated using driving speed and yaw rate. In the target steering angle calculation processing, it is judged whether the acceleration sensor is normal. If it is judged that the acceleration sensor is normal, a target steering angle is calculated by using the detected value. Otherwise, the lateral acceleration used to calculate the target steering angle is switched from the detected value to a backup value of the lateral acceleration. The backup value is calculated using the estimation value and the learning value calculated before a timing at which the acceleration sensor is judged to be abnormal.