A control system for an engine including a limiting current sensor, the control system includes an ECU configured to: execute a sweep process for gradually reducing a voltage that is applied to the sensor from a first voltage a second voltage; acquire an extreme value of an output current of the sensor during execution of the sweep process from output currents of the sensor while a voltage included in a specific voltage range is applied to the sensor, the extreme value being predicted to be output; and detect the concentration of SOx in exhaust gas based on the extreme value and a reference value, the reference value being a value of limiting current of the sensor, the value of limiting current of the sensor corresponding to the concentration of oxygen having the constant value.