In an oxygen sensor control apparatus, a CPU obtains a correction coefficient for calibrating the relation between output value of an oxygen sensor and oxygen concentration when a fuel cut operation is performed. When the amount of scavenging air (total supply amount of air) becomes equal to or greater than a predetermined amount in each fuel cut period, the CPU calculates an average output value Ipav from a plurality of output values (concentration corresponding values) Ipr of the oxygen sensor, from which values deviating from a predetermined range R1 have been removed. Subsequently, the CPU averages the values obtained in a plurality of fuel cut periods to thereby obtain a plural-time average output value Ipavf. The CPU obtains a correction coefficient for correcting the actual output value Ip of the oxygen sensor 20 on the basis of the Ipavf value and a previously set reference output value.