A steering assist apparatus for use in a vehicle steering system including right and left steering operation mechanisms that are configured to respectively steer right and left steered wheels and are respectively driven by right and left steering motors when a steering member to be manipulated to steer a vehicle in a desired direction is mechanically coupled to neither of the right and left steering operation mechanisms, characterized in that the steering assist apparatus comprises: an information acquirer configured to acquire a lateral deviation of the vehicle from a target travel line and/or a lateral deviation change rate (dy/dt), and a curvature of the target travel line, the lateral deviation change rate (dy/dt) being a rate of change in the lateral deviation per unit time; a base target steered angle setter configured to set, in accordance with the curvature of the target travel line, a left base target steered angle (δ LO *) and a right base target steered angle (δ RO *) to cause the vehicle to travel along the target travel line; a base target steered angle correction amount calculator configured to calculate a base target steered angle correction amount in accordance with the lateral deviation and/or the lateral deviation change rate (dy/dt); a turning state detector configured to detect whether the vehicle is making a right turn or a left turn; a left target steered angle correction amount setter configured to, when the vehicle is making a right turn, reduce the base target steered angle correction amount so as to set the reduced base target steered angle correction amount to be a left target steered angle correction amount, and configured to, in other states, set the base target steered angle correction amount to be the left target steered angle correction amount on an as-is basis; and a right target steered angle correction amount setter configured to, when the vehicle is making a left turn, reduce the base target steered angle correction amount so as to set the reduced base target steered angle correction amount to be a right target steered angle correction amount, and configured to, in other states, set the base target steered angle correction amount to be the right target steered angle correction amount on an as-is basis; a left target steered angle calculator configured to add the left target steered angle correction amount to the left base target steered angle (δ LO *) so as to calculate a left target steered angle; a right target steered angle calculator configured to add the right target steered angle correction amount to the right base target steered angle (δ RO *) so as to calculate a right target steered angle; a left motor controller configured to control the left steering motor in accordance with the left target steered angle; and a right motor controller configured to control the right steering motor in accordance with the right target steered angle. an information acquirer configured to acquire a lateral deviation of the vehicle from a target travel line and/or a lateral deviation change rate (dy/dt), and a curvature of the target travel line, the lateral deviation change rate (dy/dt) being a rate of change in the lateral deviation per unit time; a base target steered angle setter configured to set, in accordance with the curvature of the target travel line, a left base target steered angle (δ LO *) and a right base target steered angle (δ RO *) to cause the vehicle to travel along the target travel line; a base target steered angle correction amount calculator configured to calculate a base target steered angle correction amount in accordance with the lateral deviation and/or the lateral deviation change rate (dy/dt); a turning state detector configured to detect whether the vehicle is making a right turn or a left turn; a left target steered angle correction amount setter configured to, when the vehicle is making a right turn, reduce the base target steered angle correction amount so as to set the reduced base target steered angle correction amount to be a left target steered angle correction amount, and configured to, in other states, set the base target steered angle correction amount to be the left target steered angle correction amount on an as-is basis; and a right target steered angle correction amount setter configured to, when the vehicle is making a left turn, reduce the base target steered angle correction amount so as to set the reduced base target steered angle correction amount to be a right target steered angle correction amount, and configured to, in other states, set the base target steered angle correction amount to be the right target steered angle correction amount on an as-is basis; a left target steered angle calculator configured to add the left target steered angle correction amount to the left base target steered angle (δ LO *) so as to calculate a left target steered angle; a right target steered angle calculator configured to add the right target steered angle correction amount to the right base target steered angle (δ RO *) so as to calculate a right target steered angle; a left motor controller configured to control the left steering motor in accordance with the left target steered angle; and a right motor controller configured to control the right steering motor in accordance with the right target steered angle.