The target encirclement control of multi-robot systems via deep reinforcement learning has been investigated in this paper. Inspired by the encirclement behavior of dolphins to entrap the fishes, the encirclement control is mainly to enforce the robots to achieve a capturing formation pattern around a target, and can be widely applied in many areas such as coverage, patrolling, escorting, etc. Different from traditional methods, we propose a deep reinforcement learning framework for multi-robot target encirclement formation control, combining the advantages of the deep neural network and deterministic policy gradient algorithm, which is free from the complicated work of building the control model and designing the control law. Our method provides a distributed control architecture for each robot in continuous action space, relying only on local teammate information. Besides, the behavioral output at each time step is determined by its own independent network. In addition, both the robots and the moving target can be trained simultaneously. In that way, both cooperation and competition can be contained, and the results validate the effectiveness of the proposed algorithm.