A hybrid vehicle control device is provided with an engine stop control section and a fuel injection control section. The engine stop control section is configured to issue an engine speed reduction command to reduce an engine speed of an engine during an engine stopping operation occurring in response to establishment of an engine stop condition by using an electric motor and slip engaging a drive-wheel side clutch disposed between the electric motor and a drive wheel such that the drive-wheel side clutch transmits rotational torque between the electric motor and the drive wheel. The fuel injection control section is configured to issue a fuel injection command to continue fuel injection during the engine stopping operation until the engine speed decreases below a prescribed engine speed whereupon the fuel injection is stopped.