The recent progress in multi-agent deep reinforcement learning (MADRL) makes it more practical in real-world tasks, but its relatively poor scalability and the partially observable constraint raise more challenges for its performance and deployment. Based on our intuitive observation that human society could be regarded as a large-scale partially observable environment, where everyone has the functions of communicating with neighbors and remembering his/her own experience, we propose a novel network structure called the hierarchical graph recurrent network (HGRN) for multi-agent cooperation under partial observability. Specifically, we construct the multi-agent system as a graph, use a novel graph convolution structure to achieve communication between heterogeneous neighboring agents, and adopt a recurrent unit to enable agents to record historical information. To encourage exploration and improve robustness, we design a maximum-entropy learning method that can learn stochastic policies of a configurable target action entropy. Based on the above technologies, we propose a value-based MADRL algorithm called Soft-HGRN and its actor-critic variant called SAC-HGRN. Experimental results based on three homogeneous tasks and one heterogeneous environment not only show that our approach achieves clear improvements compared with four MADRL baselines, but also demonstrate the interpretability, scalability, and transferability of the proposed model.