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UAV cooperative control has been applied in many complex UAV communication networks. It remains challenging to develop UAV cooperative coverage and UAV energy-efficient communication technology. In this paper, we investigate current works about UAV coverage problem and propose a multi-UAV coverage model based on energy-efficient communication. The proposed model is decomposed into two steps: coverage maximization and power control, both are proved to be exact potential games (EPG) and have Nash equilibrium (NE) points. Then the multi-UAV energy-efficient coverage deployment algorithm based on spatial adaptive play (MUECD-SAP) is adopted to perform coverage maximization and power control, which guarantees optimal energy-efficient coverage deployment. Finally, simulation results show the effectiveness of our proposed approach, and confirm the reliability of proposed model.