Federated learning (FL) allows model training from local data collected by edge/mobile devices while preserving data privacy, which has wide applicability to image and vision applications. A challenge is that client devices in FL usually have much more limited computation and communication resources compared to servers in a datacenter. To overcome this challenge, we propose PruneFL -- a novel FL approach with adaptive and distributed parameter pruning, which adapts the model size during FL to reduce both communication and computation overhead and minimize the overall training time, while maintaining a similar accuracy as the original model. PruneFL includes initial pruning at a selected client and further pruning as part of the FL process. The model size is adapted during this process, which includes maximizing the approximate empirical risk reduction divided by the time of one FL round. Our experiments with various datasets on edge devices (e.g., Raspberry Pi) show that: (i) we significantly reduce the training time compared to conventional FL and various other pruning-based methods; (ii) the pruned model with automatically determined size converges to an accuracy that is very similar to the original model, and it is also a lottery ticket of the original model.