An electric waste gate valve system includes a waste gate valve, an electric actuator that drives waste gate valve, an impeller rotation speed sensor, and an electronic control unit. The waste gate valve opens and closes a bypass passage that bypasses a turbine impeller of a turbocharger. The electronic control unit is configured to calculate a predicted value of the rotation speed of the impeller when the waste gate valve is closed. The electronic control unit is configured to drive the electric actuator in a valve-closing direction to close the waste gate valve. The electronic control unit is configured to stop the driving of the waste gate valve by the electric actuator when the rotation speed of the impeller detected by the impeller rotation speed sensor increases to a reference value determined based on the predicted value.