Federated learning (FL) has sparked extensive interest in exploiting the private data on clients' local devices. However, the parameter server setting of FL not only has high bandwidth requirements, but also poses data privacy issues and a single point of failure. In this paper, we propose an efficient and privacy-preserving protocol, dubbed CFL, which is the first fine-grained global model training for FL in large-scale peer-to-peer (P2P) networks. Unlike previous FL in P2P networks, CFL aggregates local model update parameters hierarchically, which improves the communication efficiency facing large amounts of clients. Also, the aggregation in CFL is performed in a secure manner by introducing the authenticated encryption scheme, whose key is established through a random pairwise key scheme enhanced by a proposed voting-based key revocation mechanism. Rigorous analyses show that CFL guarantees the privacy and data integrity and authenticity of local model update parameters under two widespread threat models. More importantly, the proposed key revocation mechanism can effectively resist hijack attacks, thereby ensuring the confidentiality of the communication keys. Ingenious experiments on the Trec06p and Trec07 datasets show that the global model trained by CFL has good classification accuracy, model generalization, and rapid convergence rate, and the dropout-robustness of the system is achieved. Compared to the first global model training protocol for FL in P2P networks, PPT, CFL improves communication efficiency by 43.25%. Also, CFL outperforms PPT in terms of computational efficiency.