It is provided a control device of a vehicle power transmission device having an automatic transmission shifted by engagement and release of hydraulic friction engagement devices to selectively establish a plurality of gear stages and an electric motor coupled to an input shaft of the automatic transmission in a power transmittable manner, the control device executing a clutch-to-clutch shift while performing regeneration through the electric motor at the time of a coast down shift of the automatic transmission, the control device completing regenerative torque reduction control to reduce a regenerative torque of the electric motor in a torque phase of the coast down shift before start of the torque phase in accordance with a drop-off of an output torque of the vehicle power transmission device.