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Orthogonal frequency division multiplexing (OFDM) is an attractive modulation candidate for Cognitive Radio (CR) networks. Effective and reliable subcarrier power allocation in OFDM-based Cognitive Radio (CR) networks is a challenging problem. This paper focuses on the power allocation for OFDM-based Cognitive Radio (CR) networks. Our objective is to maximize the total transmission rates of Secondary Users (SU) by adjusting the power of subcarrier while the interference introduced to the Primary User (PU) is within a certain range and the total power of subcarrier is not beyond the total power constraint. We investigate the optimal power allocation algorithm for OFDM-based Cognitive Radio (CR) based on convex optimization theory. Then, because of high complexity of the optimal power allocation algorithm, we propose an effective suboptimal power loading scheme. Theory analysis and simulation results show that the performance of the suboptimal power allocation algorithm is close to the performance of the optimal power allocation algorithm, while the complexity of the suboptimal power allocation algorithm is much lower.