A control method for a turbocharger system may include controlling opening levels of an intake bypass valve, an exhaust bypass valve, and a throttle valve according to a driving condition of a vehicle by a controller, and executing a series of commands by the controller, including determining whether an engine rpm satisfies a set low/medium speed condition, determining whether an acceleration request condition is satisfied when the engine rpm satisfies the set low/medium speed condition, closing the intake bypass valve, and controlling an opening angle of the exhaust bypass valve according to the acceleration request condition.