A control device of a hybrid vehicle includes an engine, a motor/generator, a first clutch, an automatic transmission, a second clutch, and startup/shifting simultaneous processing section. When engine speed increase control for increasing the engine speed by the motor/generator in order to start up the engine during travel and downshifting control of the automatic transmission are processed in parallel, the startup/shifting simultaneous processing section uses the motor torque of the motor/generator to increase the increase of input speed by the downshifting control to a target input speed while engine speed increase control is being performed by the motor/generator.