Low encoding complexity is very important for quasi-cyclic low-density parity-check (QC-LDPC) codes used in wireless communication systems. In this paper, a new scheme is presented to construct QC-LDPC codes with low encoding complexity. This scheme is called two-stage particle swarm optimization (TS-PSO) algorithm, in which both the threshold and girth distribution of QC-LDPC codes are considered. The proposed scheme is composed of two stages. In the first stage, we construct a binary base matrix of QC-LDPC code with the best threshold. The matrix is constructed by combining a binary PSO algorithm and the protograph extrinsic information transfer (PEXIT) method. In the second stage, we search an exponent matrix of the QC-LDPC code with the best girth distribution. This exponent matrix is based on the base matrix obtained in the first stage. Consequently, the parity-check matrix of the QC-LDPC code with the best threshold and best girth distribution are constructed. Furthermore, bit error rate performances are compared for the QC-LDPC codes constructed by proposed scheme, the QC-LDPC code in 802.16e standard, and the QC-LDPC code in Tam's study. Simulation results show that the QC-LDPC codes proposed in this study are superior to both the 802.16e code and the Tam code on the additive white Gaussian noise (AWGN) and Rayleigh channels. Moreover, proposed scheme is easily implemented, and is flexible and effective for constructing QC-LDPC codes with low encoding complexity. leads to the lowest error rate. Optimization of the degree distribution pairs of irregular LDPC codes has already been considered on additive white Gaussian noise (AWGN) channels [9, 13], Rayleigh channels [11], binary erasure channels [14,15], and so on. In addition to the threshold, girth is another important parameter used to construct the LDPC codes [7]. Girth refers to the shortest cycles in the parity-check matrix or Tanner graph of LDPC codes [7,8]. The typical construction method based on girth is the progressive edge-growth (PEG) algorithm, which aims to construct the quasi-cyclic LDPC (QC-LDPC) codes by maximizing the girth of the Tanner graph of LDPC codes [16][17][18].From a practical point of view, the algebraic construction method is a good choice. The QC-LDPC code is a very important subclass of algebraic construction LDPC codes for its structured paritycheck matrix. The parity-check matrix of QC-LDPC codes is formed by the circulant permutation matrix or zero matrix, which may be easily implemented by the shift register. Consequently, QC-LDPC codes have been employed in several advanced communication standards such as 802.16e and 802.11n because of their hardware-friendly structures [1-3].The extrinsic information transfer (EXIT) chart method is another widely used method in the design of irregular LDPC codes because of its simplicity and accuracy [19,20]. However, the conventional EXIT chart method cannot be applied in the multi-edge type and protograph-based LDPC codes. To evaluate the performance of protograph LDPC codes [21], ...