A control device of a hybrid vehicle including a motive power distribution mechanism that distributes output of an engine to a first motor-generator and to an output shaft, a second motor-generator that outputs power to the output shaft via a stepped type transmission, and an electricity storage device, and a control method. In an activating operation of the vehicle, a friction engagement device is engaged, and a ready-to-run state is set based on the engagement oil pressure of the friction engagement device detected. It is determined whether the vehicle is in a motor or a non-motor run region. If the vehicle is in the non-motor run region, the original pressure of the friction engagement device is set at a non-working pressure at which a hydraulic switch does not operate, as the engine is started up. After complete explosion of the engine, the original pressure is set at a working pressure at which the switch operates.