Eliminating short cycles has been an important measure to improve Low Density Parity-Check (LDPC) codes performance, based on regular (n, 2, k) LDPC codes without short cycles, a constructing method of practical regular (n, 3, k) LDPC codes without cycle 4, 6 and 8 is proposed. The simulation results over AWGN channels prove the validity of the method, and the produced codes with girth 10 reach the outstanding performance.