This paper proposes a novel deep reinforcement learning method for constructing low-density parity-check (LDPC) codes. In this method, both deep neural network trained by reinforcement learning and Monte Carlo tree search (MCTS) are combined to discover edge growth routes without any human-defined knowledge. Due to the great ability of prediction shown by deep reinforcement learning, the proposed method has a long-term vision for constructing codes with a potential of better performance compared with the traditional computer-search-based methods. In addition, the proposed method is flexible for constructing codes with different parameters.