Federated learning (FL) is an important paradigm for training global models from decentralized data in a privacy-preserving way. Existing FL methods usually assume the global model can be trained on any participating client. However, in real applications, the devices of clients are usually heterogeneous, and have different computing power. Although big models like BERT have achieved huge success in AI, it is difficult to apply them to heterogeneous FL with weak clients. The straightforward solutions like removing the weak clients or using a small model to fit all clients will lead to some problems, such as under-representation of dropped clients and inferior accuracy due to data loss or limited model representation ability. In this work, we propose InclusiveFL, a client-inclusive federated learning method to handle this problem. The core idea of InclusiveFL is to assign models of different sizes to clients with different computing capabilities, bigger models for powerful clients and smaller ones for weak clients. We also propose an effective method to share the knowledge among multiple local models with different sizes. In this way, all the clients can participate in the model learning in FL, and the final model can be big and powerful enough. Besides, we propose a momentum knowledge distillation method to better transfer knowledge in big models on powerful clients to the small models on weak clients. Extensive experiments on many real-world benchmark datasets demonstrate the effectiveness of the proposed method in learning accurate models from clients with heterogeneous devices under the FL framework.