A control device is applied to a multi-cylinder 4-cycle charge compression ignition-type internal combustion engine. The control device operates to open an exhaust valve in an exhaust stroke of each cylinder, operates to close an intake valve before an intake bottom dead center, and then, operates to open the exhaust valve again before the intake bottom dead center. An exhaust flow rate regulating valve is disposed in a collecting portion of an exhaust path and its opening is controlled. Hereby, a period in which the exhaust valve is open in an intake stroke of one cylinder and a period in which the exhaust valve is open in an exhaust stroke of another cylinder partially overlap each other. Combustion gas pushed out of a combustion chamber of the other cylinder in the overlapping period is pushed into a combustion chamber of the one cylinder via the exhaust path.