Abstract: Combinatoric design is a potentially powerful tool for constructing good LDPC codes.In this paper，a new approach to construct regular quasi-cyclic Low-Density Parity-Check（LDPC） codes based on the difference sets is proposed.The constructed LDPC codes is free of 4-cycles and with high flexibility in the choose of the code rate.Because of their quasi-cyclic structure，the encoding can be implemented with simple feedback shift register.Simulations show that the constructed quasi-cyclic LDPC codes with Sum-product iterative decoding perform well under BPSK modulation over an Additive White Gaussian Noise（AWGN） channel.