A supercharging system comprising a pressure wave supercharger which supercharges an internal combustion engine by increasing a pressure of gas in a cell using a pressure wave of exhaust gas and discharging from an intake gas outlet port to an intake gas passage the gas pressurized further comprises a first motor which rotates a rotor, and a valve plate and a second motor capable of changing a position of the intake gas outlet port with respect to an exhaust gas inlet port. The motors are controlled so as to change a rotation number of the rotor and the position of the intake gas outlet port with respect to the exhaust gas inlet port based on a quantity of flow of exhaust gas to be recirculated to the intake gas passage.