In order to improve the communication reliability of the cognitive radio mesh network and increase spectrum utilization, a spectrum allocation algorithm based on genetic algorithm in consideration of the power control is proposed in this paper. A network utility model is built for joint power and channel allocation, and a corresponding encoding rule is designed. To ensure the validity of bodies and the fast convergence to the best solution, crossover, mutation operator and control mechanism are designed separately. Extensive simulation results are presented to verify this approach.