A hybrid vehicle control device is provided with an engine, a motor/generator, a first clutch, an automatic transmission, a second clutch, and a controller having a simultaneous process selection control section. The simultaneous process selection control section performs engine startup control and downshift control in parallel in cases where the torque outputtable by the motor subsequent to downshifting during overlap of an engine startup request and a downshift request is equal to or greater than the engine startup torque, or performs engine startup control first then downshift control in cases where the torque outputtable by the motor subsequent to downshifting is less than the engine startup torque.