A control device for hybrid vehicle drive system includes an engine rotation speed control device performing a rotation speed control of an engine so that a rotation speed of an output shaft of the engine is assumed to be equal to a next gear shift stage input shaft rotation speed when an operation amount of an accelerator pedal increases from an operation amount smaller than a first predetermined amount to an operation amount greater than a second predetermined amount, at which gear stages are switched from a current gear shift stage to a next gear shift stage whose gear ratio is greater than the current gear shift stage, within a priority determining time, a front clutch engagement commanding device, a front clutch engaging device, a release side frictional engagement element releasing device, a motor generator rotation speed control device, and an engagement side frictional engagement element engaging device.