Human mobility data offers valuable insights for many applications such as urban planning and pandemic response, but its use also raises privacy concerns. In this paper, we introduce the Hierarchical and Multi-Resolution Network (HRNet), a novel deep generative model specifically designed to synthesize realistic human mobility data while guaranteeing differential privacy. We first identify the key difficulties inherent in learning human mobility data under differential privacy. In response to these challenges, HRNet integrates three components: a hierarchical location encoding mechanism, multi-task learning across multiple resolutions, and private pre-training. These elements collectively enhance the model's ability under the constraints of differential privacy. Through extensive comparative experiments utilizing a real-world dataset, HRNet demonstrates a marked improvement over existing methods in balancing the utility-privacy trade-off.