A vehicle speed control device executes a reverse speed control that controls the speed of the vehicle when reversing, on the basis of a target speed that is set in accordance with a control operation when the reverse range is selected using the shift device of the vehicle. During the reverse speed control, the vehicle speed control device calculates so as to reduce a target acceleration. which is a target value for acceleration of the vehicle when the vehicle speed when reversing is increased toward the target speed, as the operation amount of the steering wheel increases.