An engine includes a throttle valve provided to an intake passage and a turbocharger, which includes an exhaust turbine and an intake compressor. The intake compressor is arranged in the intake passage. A waste gate valve operated using an electric actuator is provided to a bypass passage, which bypasses the exhaust turbine. A control apparatus for the engine includes a setting unit and a control unit. The setting unit sets the position of the waste gate valve at a target position in a normal operating condition of the engine. The target position is out of a position range, in which the waste gate valve is in a substantially full close position. The control unit controls the position of the waste gate valve such that the position of the waste gate valve coincides with the target position.