An adaptive subcarriers nulling power allocation algorithm for OFDM-based cognitive radio (CR) network was proposed to maximize the total capacity of CR users, with constraints on sum transmit power and the interference introduced to individual primary user on its allocated frequency band. The proposed algorithm considering both CR users' channel states and the interference to primary users (PUs) made an excellent balance between system capacity and interference reduction. Compared to the optimal power allocation algorithm, its computational complexity is significantly reduced. The simulation results show that the proposed algorithm achieves higher capacity than non-nulling power allocation algorithm. We also investigate the effect of the number of nulling subcarriers on system performance.