In an air-fuel ratio control apparatus for controlling the air-fuel ratio of an engine (1) in accordance with the output of an O2 sensor (3), in response to the starting of the engine (1) the output voltage of the 0 2 sensor (3) is sampled at intervals of a unit time. The slope of the output voltage waveform of the O 2 sensor (3) is computed from the successively sampled values. The computed value is compared with a predetermined value indicative of a slope value attained when the 0 2 sensor (3) is activated and thus it is considered that the O 2 sensor (3) is activated when the computed value is greater than the predetermined value.