Based on the construction method of systematically constructed Gallager (SCG)(4, k) code, a new improved construction method of low density parity check (LDPC) code is proposed. Compared with the construction method of SCG(4, k) codes improved before, the proposed construction method has some advantages, such as saving storage space and reducing computation complexity in the hardware implementation. And then LDPC(5929, 5624) code with 5.42% redundancy is constructed by the proposed method. The simulation results and analysis show that the constructed LDPC(5929, 5624) code has better error-correction performance, lower redundancy and lower decoding complexity than those of a classic Reed- Solomon (RS)(255, 239) code. Therefore, LDPC(5929, 5624) code, constructed by the proposed construction method on LDPC codes, can better suitable for optical transmission systems.