Visible light positioning (VLP) has drawn plenty of attention as a promising indoor positioning technique. However, in nonstationary environments, the performance of VLP is limited because of the highly time-varying channels. To improve the positioning accuracy and generalization capability in nonstationary environments, a cooperative VLP scheme based on federated learning (FL) is proposed in this paper. Exploiting the FL framework, a global model adaptive to environmental changes can be jointly trained by users without sharing private data of users. Moreover, a Cooperative Visible-light Positioning Network (CVPosNet) is proposed to accelerate the convergence rate and improve the positioning accuracy. Simulation results show that the proposed scheme outperforms the benchmark schemes, especially in nonstationary environments.