In this paper, we consider a non-orthogonal multiple access enabled cellular visible light communication network, where all users present in the network are moving based on the random way-point mobility model. According to the dynamic behavior of the network, the achievable secrecy rate of the legitimate users has been formulated. In order to allocate power to the legitimate users, the well-known gain ratio power allocation method is modified to improve the network sum secrecy rate (NSSR). The numerical results indicate that, the secrecy performance of the network is improved by employing the modified power allocation method. Furthermore, the effect of field of view (FOV) and the half-power angle have been taken into account and the simulation results show that, the NSSR depends on the FOV and the half-power angla of the optical transceivers.