We address the problem of learning structured policies for continuous control. In traditional reinforcement learning, policies of agents are learned by MLPs which take the concatenation of all observations from the environment as input for predicting actions. In this work, we propose NerveNet to explicitly model the structure of an agent, which naturally takes the form of a graph. Specifically, serving as the agent's policy network, NerveNet first propagates information over the structure of the agent and then predict actions for different parts of the agent. In the experiments, we first show that our NerveNet is comparable to state-of-the-art methods on standard MuJoCo environments. We further propose our customized reinforcement learning environments for benchmarking two types of structure transfer learning tasks, i.e., size and disability transfer. We demonstrate that policies learned by NerveNet are significantly better than policies learned by other models and are able to transfer even in a zero-shot setting.