As a basic and fundamental problem in wireless sensor network (WSN), the network coverage greatly reflects the performance of information transmission in WSN. In order to achieve a good balance between target coverage and energy consumption, in this paper, we propose a novel wireless sensor network energy efficient coverage method based on genetic algorithm. Particularly, the goal of this work is cover a 2D sensing area via selecting a minimum number of sensors. Moreover, the deployed wireless sensors should be connected to let each sensor be connected a path to the base station. Afterwards, genetic algorithm is used to compute the minimum number of potential position to let all target be k-covered and all sensor nodes be m-connected, and each chromosome is set to be the number of potential positions. Finally, we provide a simulation to test the performance of the proposed method, and simulation results demonstrate that the proposed method can achieve high degree of target coverage without wasting extra energy.