A received signal strength-based visible light positioning system with multiple light sources is investigated. In this system, each light source is assigned a unique signature code, which is constructed based on the vertex coloring of graph theory. The signature code is separated into three parts for different purposes, i.e., discriminating the beginning of the received signals, distinguishing different light sources, and correcting errors when they occur. The length of the code is determined by the numbers of the light sources. A sequential decoding scheme is devised to identify different light sources stepwisely. The light source with the highest received light intensity is discerned first by utilizing the characteristic of the signature codes. Then it is reduced from the received signals, and the remaining light sources are discriminated one by one using this scheme. With the knowledge of the coordination of these light sources, the location of the receiver can be acquired based on trilateration positioning algorithm. The simulation and the experiment results verify that the proposed signature codes can eliminate the interference from multiple sources and achieve good positioning performance.