A control apparatus for a lockup clutch is provided. The control apparatus for the lockup clutch includes an electronic control unit that is configured to: calculate a driven target clutch torque capacity and a driving target clutch torque capacity; set a target clutch torque of the lockup clutch and control the lockup clutch, based on the driven target clutch torque capacity and the driving target clutch torque capacity; and change over the target clutch torque capacity from the driven target clutch torque capacity to the driving target clutch torque capacity when the driven target clutch torque capacity and the driving target clutch torque capacity coincide with each other after an operation state of an accelerator of the vehicle changes over from an accelerator OFF state to an accelerator ON state.