To achieve change-over from detection of an internal resistance of an oxygen sensor S to detection of a threshold current effectively in a short time, a positive desired voltage for measuring a threshold current is applied to an oxygen sensor S to detect the threshold current and then a negative voltage for measuring a temperature is applied to the oxygen sensor S for a short time to detect an internal resistance of the oxygen sensor. After that, when the voltage applied to the oxygen sensor S is restored to a positive desired voltage for measuring the threshold current, by applying a voltage higher than this positive desired voltage temporarily to the oxygen sensor S, discharge or recharge of electric charges due to electrostatic capacitance components of the oxygen sensor S is completed quickly to reduce the time required for convergence to the threshold current when the voltage is changed. As a result, it is possible to reduce the time during which the threshold current cannot be detected.