An air-fuel ratio correction coefficient calculating component is provided to an air-fuel ratio controller for an engine having the wide range air-fuel ratio sensor. In order to compensate for a time lag in detection of an air-fuel ratio detected by the wide range air-fuel ratio sensor from the time when a mixed gas of the air-fuel ratio is supplied to the engine, the air-fuel ratio controller includes a component for calculating an air-fuel ratio correction coefficient to control an amount of fuel supplied to the engine based on an output signal of the air-fuel ratio sensor. The air-fuel ratio correction coefficient calculating component calculates the air-fuel ratio correction coefficient based on a nonlinear calculation element. The non-linear calculation element has an ON-OFF characteristic, a neutral zone characteristic, a saturation characteristic or a characteristic combining a plurality of characteristics selected from the above-mentioned characteristics.