Quantum key distribution (QKD) would play an important role in future information technologies due to its theoretically proven security based on the laws of quantum mechanics. How to realize QKDs among multiple users in an effective and simple way is crucial for its real applications in communication networks. In this work, we propose and demonstrate a fully connected QKD network without trusted node for a large number of users. Using flexible wavelength division multiplexing/demultiplexing and space division multiplexing, entanglement resources generated by a broadband energy-time entangled quantum light source are distributed to 40 users. Any two users share a part of entanglement resources, by which QKD is established between them. As a result, it realizes a fully connected network with 40 users and 780 QKD links. The performance of this network architecture is also discussed theoretically, showing its potential on developing quantum communication networks with large user numbers owing to its simplicity, scalability, and high efficiency.