In order to improve the performance of visible light communication (VLC) systems, a novel construction method of quasi-cyclic low-density parity-check(QC-LDPC) codes is proposed to solve the problem that the minimum distance between code words of QC-LDPC codes is not large enough, which leads to the degradation of the error correction performance. In the proposed construction method, the information bit of QC-LDPC codes is constructed by combining the greatest common divisor (GCD) algorithm with Lucas sequence. At the same time, in order to reduce the encoding complexity, the check bit is designed in the form of the quasi-double diagonal, which can ensure the large girth length and realize the fast encoding of QC-LDPC codes. Then the GL-QC-LDPC (2650,1325) code with a code rate of 0.5 is constructed with the proposed construction method, and the simulation performance is analyzed in the established VLC system simulation model. Simulation results show that at the bit error rate(BER) of 10-6, the net coding gain(NCG) of the GL-QC-LDPC(2650,1325) code constructed by this method is respectively 0.10, 0.14 and 0.25dB more than those of AC-QC-LDPC(2652,1326) code based on the array codes(AC), GM-QC-LDPC (2650, 1325) code constructed directly using the GCD algorithm and the modification technology and GDD-QC-LDPC (2652, 1326) code based on group divisible designs (GDD).