A steer-by-wire steering system for a vehicle, comprising: an operation member operable by a driver; a reaction force applying device configured to apply an operation reaction force to the operation member ; a steering device configured to steer a wheel ; and a controller configured to control the reaction force applying device and the steering device , wherein the controller is configured to execute: a steering control process in which the controller determines a steering gear ratio and controls the steering device such that a ratio of a steering amount of the wheel with respect to an operation amount of the operation member becomes equal to the steering gear ratio; a converted operation amount determining process in which the controller converts an actual steering amount of the wheel to the operation amount of the operation member based on an inverse of the determined steering gear ratio, so as to determine a converted operation amount; and a reaction force control process in which, based on an operation amount deviation that is a difference between an actual operation amount of the operation member and the converted operation amount, the controller controls the reaction force applying device such that the operation reaction force increases with an increase in the operation amount deviation, characterised in that in the converted operation amount determining process, when the determined steering gear ratio abruptly changes, the controller converts, based on the steering gear ratio, a gap of the converted operation amount generated at a time point of occurrence of the abrupt change to a gap of the steering amount of the wheel , so as to grasp the gap of the steering amount of the wheel as a converted steering amount offset value, the controller thereafter re-converts the converted steering amount offset value to the gap of the converted operation amount based on the inverse of the steering gear ratio while gradually decreasing the converted steering amount offset value, so as to determine a converted operation amount correction value, and the controller corrects the converted operation amount based on the converted operation amount correction value. a steering control process in which the controller determines a steering gear ratio and controls the steering device such that a ratio of a steering amount of the wheel with respect to an operation amount of the operation member becomes equal to the steering gear ratio; a converted operation amount determining process in which the controller converts an actual steering amount of the wheel to the operation amount of the operation member based on an inverse of the determined steering gear ratio, so as to determine a converted operation amount; and a reaction force control process in which, based on an operation amount deviation that is a difference between an actual operation amount of the operation member and the converted operation amount, the controller controls the reaction force applying device such that the operation reaction force increases with an increase in the operation amount deviation, characterised in that in the converted operation amount determining process, when the determined steering gear ratio abruptly changes, the controller converts, based on the steering gear ratio, a gap of the converted operation amount generated at a time point of occurrence of the abrupt change to a gap of the steering amount of the wheel , so as to grasp the gap of the steering amount of the wheel as a converted steering amount offset value, the controller thereafter re-converts the converted steering amount offset value to the gap of the converted operation amount based on the inverse of the steering gear ratio while gradually decreasing the converted steering amount offset value, so as to determine a converted operation amount correction value, and the controller corrects the converted operation amount based on the converted operation amount correction value. <EOS>