An oxygen supply apparatus and method for a fuel cell of an aircraft are provided. The oxygen supply apparatus includes a compressor that generates compressed air by compressing air in the atmosphere and supplies the compressed air to a fuel cell stack, an oxygen tank having a predetermined amount of oxygen stored therein. An aircraft monitoring device monitors the aircraft and determines whether oxygen supply from the oxygen tank is required, and an oxygen supply means switching device switches an oxygen supply means for the fuel cell stack from the compressor to the oxygen tank, or vice versa depending on an outcome of the monitoring.