A power transmission device for a hybrid vehicle, comprising: a power distribution mechanism which includes a plurality of rotation components rotating in different rotation speeds and in which a rotation shaft of an engine, a rotation shaft of a first rotary machine, a rotation shaft of a second rotary machine, and a drive wheel are respectively connected to four rotation components among the rotation components; a friction engagement device which is interposed between the engine and the rotation component connected to the engine; and a control device (HVECU) which performs a stop control for the engine and a release control for the friction engagement device so as to cause the vehicle to travel only by the power of the second rotary machine and performs an engagement control for the friction engagement device while the vehicle travels only by the power of the second rotary machine so as to perform a push-start of the engine, wherein the control device (HVECU) is configured to control the first rotary machine so that the friction engagement device is maintained in a half engagement state at a differential rotation speed higher than a predetermined rotation speed during the push-start of the engine, characterized in that when a vehicle speed is equal to or higher than a predetermined vehicle speed during the push-start of the engine, the control device (HVECU) controls the friction engagement device in the half engagement state and controls the rotation speed of the first rotary machine in the reverse rotation direction, when vehicle speed is lower than the predetermined vehicle speed during the push-start of the engine, the control device (HVECU) controls the friction engagement device in the half engagement state and controls the rotation speed of the first rotary machine in the forward rotation direction, and when the differential rotation speed of the friction engagement device decreases to the predetermined rotation speed after the control in the reverse rotation direction or the forward rotation direction, the control device (HVECU) controls the rotation speed of the first rotary machine in the forward rotation direction. a power distribution mechanism which includes a plurality of rotation components rotating in different rotation speeds and in which a rotation shaft of an engine, a rotation shaft of a first rotary machine, a rotation shaft of a second rotary machine, and a drive wheel are respectively connected to four rotation components among the rotation components; a friction engagement device which is interposed between the engine and the rotation component connected to the engine; and a control device (HVECU) which performs a stop control for the engine and a release control for the friction engagement device so as to cause the vehicle to travel only by the power of the second rotary machine and performs an engagement control for the friction engagement device while the vehicle travels only by the power of the second rotary machine so as to perform a push-start of the engine, wherein the control device (HVECU) is configured to control the first rotary machine so that the friction engagement device is maintained in a half engagement state at a differential rotation speed higher than a predetermined rotation speed during the push-start of the engine, characterized in that when a vehicle speed is equal to or higher than a predetermined vehicle speed during the push-start of the engine, the control device (HVECU) controls the friction engagement device in the half engagement state and controls the rotation speed of the first rotary machine in the reverse rotation direction, when vehicle speed is lower than the predetermined vehicle speed during the push-start of the engine, the control device (HVECU) controls the friction engagement device in the half engagement state and controls the rotation speed of the first rotary machine in the forward rotation direction, and when the differential rotation speed of the friction engagement device decreases to the predetermined rotation speed after the control in the reverse rotation direction or the forward rotation direction, the control device (HVECU) controls the rotation speed of the first rotary machine in the forward rotation direction.