An air-fuel ratio sensor control apparatus comprises a voltage control part configured to control a voltage Vo1 applied to a cell of an air-fuel ratio sensor in accordance with a sensor current flowing in the cell and a current detection part configured to detect the sensor current as a physical value, which indicates the air-fuel ratio. In the air-fuel ratio sensor control apparatus, a voltage varying time point, at which the voltage control part varies the voltage Vo1, and a current detecting time point, at which the current detection part detects the current, are shifted from each other. A time period Ta from the current detecting time point, which is immediately before the voltage varying time point, to the voltage varying time point and a time period Tb from the voltage varying time point to the current detecting time period, which is immediately after the voltage varying time point, are set to satisfy Ta