Deriving a distributed, time-efficient, and connectivity guaranteed coverage policy in multi-target environment poses huge challenges for a multi-robot team with limited coverage and limited communication. In particular, the robot team needs to cover multiple targets while preserving connectivity. In this paper, a novel deep reinforcement learning based approach is proposed to take both multi-target coverage and connectivity preservation into account simultaneously, which consists of four parts: a hierarchical observation attention representation, an interaction attention representation, a two-stage policy learning, and a connectivity guaranteed policy filtering. The hierarchical observation attention representation is designed for each robot to extract latent features of the relations from its neighboring robots and the targets. To promote the cooperation behavior among the robots, the interaction attention representation is designed for each robot to aggregate information from its neighboring robots. Moreover, to speed up the training process and improve the performance of the learned policy, the two-stage policy learning is presented using two reward functions based on algebraic connectivity and coverage rate. Furthermore, the learned policy is filtered to strictly guarantee connectivity based on a model of connectivity maintenance. Finally, the effectiveness of the proposed method is validated by numerous simulations. Besides, our method is further deployed to an experimental platform based on quad-rotor unmanned aerial vehicles (UAVs) and omnidirectional vehicles. The experiments illustrate the practicability of the proposed method.