Indoor Positioning techniques are fundamental for many modern techniques and applications, such as internet of things, smart home, robot navigation, et al. To achieve positioning in indoor environments, wireless techniques, such as radio frequency identification, WiFi, Bluetooth, and ultra-wideband, are commonly considered. As an alternative, the visible light communication technique is promising for indoor positioning due to advantages such as deployments, source. In this work, we first investigate the propagation of the light signal in indoor environments. The Gaussian process method is then proposed to characterize the received power traveling through both the line-of-sight path and the reflected path. We use kernel functions to model the spatial correlation nature for the reflected lights. Based on that, target location estimates are given by the Bayesian inference both in a discrete setup and a continuous framework, which are the probabilistic fingerprinting and the maximum likelihood estimate. We conduct practical experiments to validate the proposed Gaussian process model. The regression results and positioning performances are studied against the size of training data.