A control device of a vehicle comprises: an electric motor connected to a drive force transmission path through a first connecting/disconnecting device connecting/interrupting power transmission; and an engine connected to the electric motor through a second connecting/disconnecting device connecting/interrupting power transmission, the control device of a vehicle disconnecting the first connecting/disconnecting device or the second connecting/disconnecting device during running to perform coasting with the engine separated, when performing coasting, a determination whether a vehicle speed is equal to or lower than a predetermined determination vehicle speed implemented, the engine separated by disconnecting the second connecting/disconnecting device with the first connecting/disconnecting device kept connected at a low vehicle speed where the vehicle speed is equal to or lower than the predetermined determination vehicle speed, and the engine separated by disconnecting the first connecting/disconnecting device at a high vehicle speed where the vehicle speed is higher than the predetermined determination vehicle speed.