A novel architecture of a visible light communication (VLC) network that can provide bidirectional transmission for multiple users is proposed in this paper. Multiple users can exchange data asynchronously and simultaneously thanks to the use of analog network coding (ANC) and optical code division multiple access (OCDMA) with the support of a coordinator, which plays a role as a relay node. We derive the mathematical expressions for bit error rate (BER) and network throughput of an indoor VLC network with multiple users located in a room and one coordinator mounted on the ceiling. Many physical layer impairments are considered in our analysis, including shot noise, thermal noise, multiuser interference (MUI), and optical beat noise. BER and throughput performance are investigated versus the transmitted optical power, the number of users, and the VLC transceiver’s parameters. The numerical results obtained in this paper will provide useful information for designing the indoor multiuser VLC networks.