A catalyst oxygen purge control method may include a catalyst oxygen purge control method during a cold engine period of a catalyst oxygen purge control apparatus which includes a three way catalytic converter through which an exhaust gas combusted when air and fuel are mixed in a combustion chamber is exhausted and the exhaust gas passes, wherein the method includes determining whether a fuel cut condition of an injector which injects the fuel to the combustion chamber is satisfied, performing fuel cut of the injector when the fuel cut condition is satisfied, measuring an oxygen storage capacity of the three way catalyst, and adjusting an oxygen purge time based on the measured oxygen storage capacity.