A control device for a hybrid vehicle automatic transmission. The hybrid vehicle being capable of EV travel in which drive wheels are driven by only a rotary electric machine with the internal combustion engine stopped. The control device having an electric oil pump control device to drive an electric oil pump that supplies oil to the friction engagement element. A neutral control device performs disengagement control on the friction engagement element. A drag determination device determines whether conditions under which drag of the friction engagement element occurs are met because of a shortage in amount of oil to be supplied to a cancellation oil chamber of the friction engagement element by the electric oil pump during the EV travel started from a state in which the hybrid vehicle is stationary. Drag elimination control device provides a command to start the internal combustion engine.