In OFDM communication systems, frequency offsets may distort the orthogonality between subcarriers, and then result in intercarrier interference (ICI). This paper presents a new ICI cancellation scheme for combating the impact of ICI on OFDM systems. Its main idea is repeated symbol and interference self-cancellation. That is, two repeated symbol blocks, in which the 1st block is similar to a conventional OFDM system, but the 2nd block is formed by cyclic right shift of the 1st block, are respectively transmitted at the transmitter. At the receiver, the received signal is demodulated and divided into two paths corresponding to the two transmitted symbol blocks. The two symbol streams are combined to obtain the estimation of original data symbols. Analysis results show that the ICI contained in received signals can be efficiently reduced, and the carrier-to-interference power ratio (CIR) of this scheme is at least 10 dB better than that of a conventional OFDM system. Meanwhile, simulation results show that the bit error rate (BER) of this scheme has obvious improvements comparing with a conventional OFDM system and a similar scheme in various channel environments. Consequently, this scheme can remarkably improve the performance of OFDM communication systems due to frequency offsets