Cooperative unmanned aerial vehicles (UAVs) cluster technology is considered a prospective solution for area coverage problems, enabling network access and emergency communications in remote areas. In this paper, we investigate how to control UAV cluster to achieve long-term and stable regional coverage while maintaining link connectivity and minimizing energy consumption, given the limited communication range and energy consumption of the UAVs themselves. To this end, we propose a cooperative UAV cluster strategy based on multi-agent deep reinforcement learning (MADRL) to achieve fair coverage of communication regions, which we call MADRL-based cooperative UAV cluster strategy (MADRL-CUCS). Our solution is a centralized training distributed execution architecture and defines a cluster structure for leader UAVs and follower UAVs. Under the premise of comprehensively considering the maximum coverage, we use a new energy efficiency function to minimize energy consumption, so as to extend the network lifetime of the UAVs cluster networks. The new fairness index and collision avoidance factor are used to ensure that the UAV cluster achieve effective and secure regional coverage. We adopt depth first search algorithm to check the link connectivity of the UAVs during the coverage process. Experiments show that the MADRL-CUCS algorithm outperforms the benchmark algorithm.