Abstract: Quasi-cyclic LDPC code is a kind of half-structured low density parity check code. Its block-based property leads to highly structured integrated circuits implementation, without significant performance loss. An algorithm searching shift values for the nonzero entries in base matrix of a Quasi-cyclic LDPC code is proposed along with its improved version. By expanding the Tanner graph of the corresponding expansion matrix, cycles with given length can be detected. Unlike some former algorithms, arithmetic operations are avoided, which leads to a considerable complexity reduction. Given the same base matrix with code rate 0.5 as is used in the IEEE 802.16e standard, LDPC codes constructed by the proposed algorithms have better cycle distributions and achieve slightly improved error-correction performance than the IEEE 802.16e LDPC code as well.