Cognitive visible light communication (VLC) has attracted increasing attention. By sharing underutilized VLC spectrum resources of primary users (PUs) with secondary users (SUs) opportunistically, improved spectrum utilization can be achieved without interfering with PUs. As an essential component in cognitive VLC, reliable spectrum sensing is crucial to ensure accurate cognition of PU's signal. However, due to limiting factors such as low signal-to-noise ratio (SNR) and link blocking in VLC systems, it would be difficult for a single SU to identify the status of PUs accurately and rapidly. To tackle this issue, we propose a new collaborative sensing (CS) scheme which can enhance sensing accuracy effectively by coordinating multiple SUs to participate in spectrum sensing. To evaluate the performance of the proposed CS scheme, we first develop an analytical model for the scenario of a single SU, subject to various factors such as indoor reflections and signal sampling size. Next, based on the single-SU evaluation, we further analyze the performance of the CS scheme by extending the single-SU analytical models to the multi-SU scenario. It is found that the analytical models can accurately predict the performance of the proposed CS scheme and match the results obtained by simulations. Moreover, the proposed CS scheme is effective in improving the sensing accuracy by about 40% and 10% compared with the local-sensing and the conventional CS schemes, respectively.