Abstract: Full diversity Low Density Parity Check (LDPC) codes construction is the hot spot in LDPC field at present. Traditional construction algorithm designs column full rank check submatrix to realize full diversity LDPC codes under ML decoding algorithm. However, under BP decoding algorithm, the LDPC codes designed based on ML principle can not guarantee full diversity. In this paper, the construction method of full diversity LDPC codes under BP decoding algorithm is first put forward by changing the structure of parity check matrix, then, density propagetion process of full diversity LDPC codes is analyzed. Finally, the relationship between the structure of full diversity LDPC codes and the coding gain is researched, and the algorithm to improve coding gain is given. Simulation results show that the proposed algthriom can not only achieve full diversity, but also get better performace than random constructed LDPC codes.