Abstract: Dynamic spectrum allocation is a key technology of the cognitive radio. In this paper, a new spectrum allocation algorithm for cognitive radio is proposed based on the analysis of the OFDM based cognitive radio system. For this system that the constant rate users and the variable rate users were coexistence with each other, the proposed algorithm is minimizing the transmitted power per bit, allocating the free spectrum in the cognitive radio cell dynamically in a sense of fair maximization. The system object function is simplified by using the min-max criterion and the multi-step method. Simulation results are presented to confirm the performance of the proposed algorithm. It’s achieves not only the fair allocation of the spectrum resource but also the balance between the power minimization of the constant rate users and the throughput maximization of the variable rate users, it’s suitable for the situation that there exist two kinds of users in the cognitive radio system.