A control device for a power transmission device including an automatic transmission and a sub transmission is provided. The control device includes an electronic control unit. The electronic controlunit is configured to perform a rotation speed decrease control in which at least one frictional engagement device is controlled to be an engaged state or a semi-engaged state at a time when switchingof gear stage of the sub transmission is started or a time when the switching is started. The electronic control unit is configured to end the rotation speed decrease control during switching of thegear stage. The electronic control unit is configured to switch the sub transmission from the power transmission cutoff state to a state in which one of the high-speed engagement element and the low-speed engagement element is engaged, during disengagement of the at least one frictional engagement device.