A control apparatus for a hybrid vehicle drive system including: a differential device provided with rotary elements respectively connected to an engine, first and second electric motors and an output rotary member; a brake for selectively fixing the rotary element connected to the first electric motor, to a stationary member; and a parking-lock mechanism preventing a rotary motion of a parking-lock gear connected to the output rotary member, when a manually-operated shifting device is operated to a parking-lock position. The control apparatus includes an engine starting control-portion configured to start the engine in a starting-mode wherein an operating speed of the engine is raised with a torque generated by the second electric motor in an engaged state of the brake, where the engine is required to be started while the vehicle has been held at rest and the rotary motion of the parking-lock gear is prevented by the parking-lock mechanism.