Low-Density Parity-Check (LDPC) codes are considered among the best error-correcting codes in use today. These codes can be defined by a sparse parity-check matrix H, which has a graphical representation as a Tanner graph. Several studies have shown that the existence of 4-cycles in the Tanner graph affects the performance of LDPC codes. In this paper, we propose a method which allows the construction of 4-cycle-free parity-check matrices. The main principles behind the proposed method are as follows: First, we choose a vector V which consists of w_c ones and L-w_c zeros, in such a way that the chosen vector allows us to construct a circulant matrix H₁ without 4-cycles. Second, we pass this matrix to the proposed algorithm to obtain a set of L-vectors. When any vector taken from this set is appended as a news column in the matrix H₁, we obtain an L×(L+1) matrix without 4-cycles. Next, we select those vectors that lead to a circulant matrix H_{2 without 4-cycles. Finally, we can obtain an L×2L matrix H without 4-cycles by concatenating matrices H1 and H2. Simulation results confirm that the structure of the matrices constructed by the proposed method significantly reduces the encoding complexity. Though the performance of these matrices at higher signal-to-noise-ratios (SNRs) is not as good as those constructed by MacKay’s method, they can be applied to practical communications because of being encoded in linear time with shift registers.}