A hybrid vehicle control device includes an engine start control unit which, at engine start, starts slipping a second clutch, sets a first clutch to a slip-engaged state, and sets the second clutch transmission torque capacity to less than or equal to a set torque limit value during cranking, maintains the slip state and cranks the engine, and when the engine is put in a drive state, controls the first clutch and the second clutch towards a fully engaged state. The engine start control unit is provided with a second clutch torque increase gradient control unit which, when performing cranking processing, performs first increasing processing for increasing the second clutch transmission torque capacity command value at a first increase gradient, and second increasing processing for increasing said value at a second increase gradient more gradual that the first increase gradient.