This paper gives the balanced incomplete block designs with the block sizes of 3,4 and 5,three kinds of LDPC(low-density parity-check code)are constructed using the designed incidence matrices as check matrices.Since these check matrices are quasi-cyclic matrices,the constructed code are QC-LDPC(quasi-cyclic LDPC).The relevant parameters of the codes are calculated and through the analysis and comparison of decoding performance with random-like codes based on specific examples,the results show that proposed codes in this paper have better performance.