It is provided a control device of a hybrid vehicle having a damper device disposed in a power transmission path between an engine and an electric motor, the damper device having different torsion characteristics between torsion in positive direction in which drive power is transmitted from the engine toward the electric motor and torsion in negative direction in which drive power is transmitted from the electric motor toward the engine, the control device being configured to increase rotation of the engine with the electric motor to start the engine, the torsion characteristic in the negative direction of the damper device including a plurality of torsion characteristics having torsional rigidity varying depending on an angle of the torsion, and at start of the engine, the plurality of torsion characteristics being selectively used depending on an engine rotation speed to increase the engine rotation speed.