A system for controlling an exhaust gasdriven supercharger used in an internal combustion engine for an automotive vehicle includes an exhaust gas bypass passage (48) connecting between selected portions of the exhaust gas conduit upstream and downstream of a turbine (44) of the supercharger (42), and an exhaust bypass valve (50) disposed midway of the exhaust gas bypass passage (48) for controlling the quantity of engine exhaust gases. In the supercharger control system, an actuator (52) responsive to a digital control signal is employed for actuating the exhaust bypass valve (50). A microcomputer (100) calculates the opening of the exhaust bypass valve (50) so that the supercharged air pressure may not exceed the critical point giving rise to knocking, and such a digital control output signal is applied to energize the actuator (52) so that the supercharged air pressure can be controlled with highest efficiency over a wide operation range of the engine.