Abstract: This paper constructs Partially Balanced Incomplete Block Designs（PBIBD） based on finite fields，and uses them to construct regular Low-Density Parity-Check（LDPC） codes.The constructed LDPC codes are free of 4-cycles and with high flexibility for the choosing of the code rate.Further，the paper even constructs QC-LDPC codes with girth at least 8，they can also be quasi-cyclic.Simulation results show that some of the codes can have slightly better performance than random regular LDPC codes over AWGN channel.