High performance of visible light communication (VLC) systems requires overcoming the limitations imposed by the optical wireless channel distortions resulting from path loss and temporal dispersion. In order to design techniques to combat the effects of channel distortions, an accurate VLC channel model is needed. In this paper, we propose a new regular-shaped geometry-based multiple bounce model (RS-GBMB) for VLC channels. The proposed model employs a combined two-ring model and ellipse model, where the received signal is constructed as a sum of the line-of-sight (LoS), single-, double-, and triple bounced rays of different powers. This makes the model sufficiently generic and adaptable to a variety of indoor scenarios. Based on the proposed RS-GBMB model, statistical properties are then investigated, such as the channel DC gain, mean excess delay, root mean square (RMS) delay spread, and Rician factor.