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In this paper, we present and analyze an interference avoidance scheme for OFDM cognitive radio systems. From an active suppression point of view, it effectively prevents the negative effect of intercarrier interference that a cognitive radio may inflict on primary transmission due to frequency offset. At the same time, it ensures bandwidth efficiency of secondary transmission. Based on the least square error criterion, it is robust to frequency offset estimation error and has a low computational complexity. Furthermore, its generalized form and algorithm can simply adapt to different frequency offsets and be extended to multiple users' case. Simulation results show the enhanced performance of our proposed scheme, which greatly reduces the interference power in comparison with the passive tone null scheme.