A shift range control apparatus controls a shift range switching system that switches shift ranges by controlling driving of a motor. This control apparatus calculates a motor angle based on a motor rotation angle signal, acquires an output shaft signal based on a rotation position of an output shaft from an output shaft sensor, sets a target rotation angle based on a target shift range and the output shaft signal, and controls driving of the motor such that the motor angle becomes the target rotation angle. The control apparatus sets the target rotation angle to a target limit value, in response to the target rotation angle that is set based on the output shaft signal being a value at which rotation occurs that is further toward a back side in a rotation direction than the target limit value that is set based on shift ranges before and after switching.