With the rapid development of wireless sensor network (WSN), the demands of limited radio frequency spectrum rise sharply, thereby dealing with the frequency assignment of WSN scientifically and efficiently becomes a popular topic. To improve the frequency utilization rate in WSN, a spectrum management system for WSN combined with cloud computing technology should be considered. From the optimization point of view, the study of dynamic spectrum management can be divided into three kinds of methods, including Nash equilibrium, social utility maximization, and competitive economy equilibrium. In this paper, we propose a genetic algorithm based approach to allocate the power spectrum dynamically. The objective is to maximize the sum of individual Shannon utilities with the background interference and crosstalk consideration. Compared to the approach in [1], the experimental result shows better balance between efficiency and effectiveness of our approach. With the rapid development of wireless sensor network (WSN), the demands of limited radio frequency spectrum rise sharply, thereby dealing with the frequency assignment of WSN scientifically and efficiently become a popular topic. To improve the frequency utilization rate in WSN, a spectrum management From the optimization point of view, the study of dynamic spectrum management can be divided into three kinds of methods, including Nash equilibrium, social utility maximization, and competitive economy equilibrium. In this paper , than the approach of allocating the power spectrum dynamically. Compared to the approach of allocating the power spectrum dynamically, the objective is to maximize the sum of individual power with the background interference and crosstalk consideration. Compared to the approach in [1] efficiency and effectiveness of our approach.