To enhance a controllability in an air-fuel ratio feed back control using an oxygen sensor by switching/controlling an air-fuel ratio detection characteristic by the oxygen sensor.

The air-fuel ratio feed back control of an engine is provided with a heater for heating an element of the oxygen variable-density battery type oxygen sensor. At the condition that a temperature of cooling water just after starting is low, the heater is controlled such that the oxygen sensor becomes a relatively low temperature (300-400°C) indicating a stoichi characteristic so as to avoid a generation of a thermal impact caused by a deposited moisture content and an air fuel ratio is feedback-controlled from rich lean against a theoretical air-fuel ratio. Whereas, at the condition that it is presumed that a generation of the thermal impact caused by the deposited moisture content does not exist, the heater is controlled such that the oxygen sensor becomes a relatively high temperature (700-800°C) indicating a linear characteristic near the theoretical air-fuel ratio and the air-fuel ratio is feedback-controlled from a deviation of the actual air-fuel ratio against the target air-fuel ratio.