A hybrid vehicle driving device includes: a first motor generator; a second motor generator; an input shaft; an output shaft; a rotating member rotatably linked to the output shaft; a connection member to which the first motor generator is connected; a connection mechanism which connects and disconnects the connection member and the rotating member; a one-way clutch connecting the input shaft and the connection member; a synchronization control portion synchronizing the rotational speed of the first motor generator with the rotational speed of the rotating member; a first engine control portion maintaining the rotational speed of an engine; a connection portion connecting the connection member and the rotating member to each other; and a second engine control portion controlling the engine such that the rotational speed of the input shaft is synchronized with the rotational speed of the connection member.