A power transmission apparatus for a vehicle which includes a first, a second, and a third rotor which split power among a motor-generator, an internal combustion engine, and a driven wheel of the vehicle. The apparatus also includes a torque transmission control mechanism which selectively transmits torque between the first rotor and the engine. When the torque transmission control mechanism establishes the transmission of torque between the first rotor and the engine, powers, as produced by the second and third rotors, are opposite in sign to each other. This enables the speed of the first rotor to be set to zero (0) or a very low speed. Therefore, when an initial torque is applied to the engine through the first rotor to start the engine, the mechanical vibration which usually arises from the application of initial torque and is to be exerted on the power transmission apparatus is minimized.