It is provided a control device for a vehicle power transmission device having a stepped automatic transmission making up a portion of a power transmission path between an engine and a drive wheel, the control device setting a shift point of the automatic transmission in accordance with a request drive force of a driver and a vehicle speed, the control device setting a shift point of the automatic transmission in accordance with a rotation speed of the engine and a vehicle speed instead of the request drive force, if a vehicle is in a predetermined fuel consumption priority running state.