This paper proposes a novel indoor positioning algorithm using visible light communications (VLC). The algorithm is implemented by preinstalled light-emitting diode illumination systems. It recovers the VLC channel features from illuminating visible light and estimates receiver locations by analytically solving the Lambertian transmission equation group. According to our research, the algorithm is able to provide positioning resolution higher than 0.5 mm, in a practical indoor environment. The performance significantly exceeds conventional indoor positioning approaches using microwaves.