A hybrid vehicle control device is provided with at least one controller programmed to control outputs of the engine and the electric motor, an engagement and disengagement of the clutch, and a transmission ratio of the continuously variable transmission in accordance with a driving state. The at least one controller is further programmed to restart the engine while maintaining a released state of the clutch, and downshift the continuously variable transmission to a predetermined transmission ratio for passing over the level difference upon determining that the level difference is present while traveling by a drive force of the motor with the clutch released and the engine stopped.