A joint power and sub-channel resource allocation algorithm was designed for orthogonal frequency division multiplexing (OFDM) based multi-colour visible light communication (VLC) systems. Compared to the conventional monochromatic optical communication system, this algorithm could be used for OFDM signal transmission of multiple visible lights including red, green and blue. The proposed algorithm aimed to maximize the transmission rate of the visible light transmission network. The optimally allocation of sub-channels was first performed for three different visible lights. After obtaining this optimized sub-channel value, the power was allocatied to it in order to achieve the final target optimized value. Simulation results show that the algorithm can achieve higher transmission rate than fixed resource allocation algorithms.