In visible light communication (VLC) systems, the amplitude of the modulated transmit signal must be nonnegative to drive light-emitting diodes to illuminate, resulting in a very different achievable rate formula of VLC system compared to that of a traditional radio frequency system. Therefore, the traditional precoding matrix design method for maximizing the achievable rate is no longer applicable. In terms of the issue, this study proposes a precoding matrix design method for multiple input multiple output VLC systems. First, it is based on the strict Karush-Kuhn-Tucker conditions to achieve the eigen-channel power allocation expression. Then, the water-filling algorithm ensures that the subchannels with better performance are allocated higher power. The method can achieve the optimal achievable rate with low complexity characteristics by constraining the order of eigen-channel power values. The simulation results show that the achievable rate index of the method is significantly improved, compared with the existing precoding matrix design methods.