Mobile apps, such as mHealth and wellness applications, can benefit from deep learning (DL) models trained with mobile sensing data collected by smart phones or wearable devices. However, currently there is no mobile sensing DL system that simultaneously achieves good model accuracy while adapting to user mobility behavior, scales well as the number of users increases, and protects user data privacy. We propose Zone-based Federated Learning (ZoneFL) to address these requirements. ZoneFL divides the physical space into geographical zones mapped to a mobile-edge-cloud system architecture for good model accuracy and scalability. Each zone has a federated training model, called a zone model, which adapts well to data and behaviors of users in that zone. Benefiting from the FL design, the user data privacy is protected during the ZoneFL training. We propose two novel zone-based federated training algorithms to optimize zone models to user mobility behavior: Zone Merge and Split (ZMS) and Zone Gradient Diffusion (ZGD). ZMS optimizes zone models by adapting the zone geographical partitions through merging of neighboring zones or splitting of large zones into smaller ones. Different from ZMS, ZGD maintains fixed zones and optimizes a zone model by incorporating the gradients derived from neighboring zones' data. ZGD uses a self-attention mechanism to dynamically control the impact of one zone on its neighbors. Extensive analysis and experimental results demonstrate that ZoneFL significantly outperforms traditional FL in two models for heart rate prediction and human activity recognition. In addition, we developed a ZoneFL system using Android phones and AWS cloud. The system was used in a heart rate prediction field study with 63 users for 4 months, and we demonstrated the feasibility of ZoneFL in real-life.