A control device of a vehicle provided with an engine, and a fluid-operated power transmitting device provided with a lock-up clutch and configured to transmit a drive force of said engine to drive wheels, and an engine connecting/disconnecting clutch configured to selectively place a power transmitting path between said engine and said fluid-operated power transmitting device in a power transmitting state and a power cutoff state, said vehicle being able to run in an engine drive mode in which said engine is operated as a vehicle drive power source while said engine connecting/disconnecting clutch is placed in a fully engaged state, comprising: a lock-up clutch control portion configured to bring said engine connecting/disconnecting clutch from the fully engaged state into a slipping state and temporarily place the engine connecting/disconnecting clutch in the slipping state while said lock-up clutch is placed in a slipping state, when a lock-up slip control is implemented to place said lock-up clutch from a fully released state into the slipping slip and gradually bring the lock-up clutch into a fully engaged state, in response to an increase of a required amount of acceleration of said vehicle, during running of the vehicle in said engine drive mode with said engine connecting/disconnecting clutch being placed in the fully engaged state.