An OFDM system using cross-handed circular Polarization(XCP-OFDM) is newly proposed in his paper. The proposed XCP-OFDM system divides the subchannels into a right-handed circular polarization(RHP channel and a left-handed circular polarization(LHCP) channel that alternate each other. Therefore, the overlaps between subcarriers in XCP-OFDM system can be reduced to a great extend compared to the conventional OFDM system. By this reason, it can improve the orthogonality and reduce the inter-channel interference due to frequency offset. In this paper, it can be seen that the proposed XCP-OFDM system shows robust against frequency offset.