Control device of hybrid vehicle including an engine connected via a clutch to power transmission path and a rotator acting at least as an electric motor, hybrid vehicle being configured to execute an engine running mode in which clutch is engaged to use at least engine as a drive force source for running and a motor running mode in which clutch is released to use rotator as drive force source for running, control device putting clutch into slip engagement to crank and start engine before clutch is completely engaged at time of switching to engine running mode during stop of engine with clutch released, control device of hybrid vehicle, when clutch temperature reaches predefined value at time of switching to the engine running mode, releasing clutch and causing rotator to generate drive force for running while controlling rotation speed of engine to synchronize rotation speeds before and after clutch.