This paper presents a construction met hod of quasi-cyclic non-binary low density parity-check (NB-LDPC) code based on the finite field three-dimensional construction.After construction of base matrix based on the finite field,a cyclic matrix is constructed with the method of three-dimensional exte nsion.Finally,non-binary parity check matrix with quasi-cyclic feature is constructed.Compared wit h the GF(2⁹)-based RS(511,5) and NB-LDPC code constructed by the three-dimensional construction can increase 3.3dB net code gain (NCG) at the bit error rate (BER) of 10－7.Compare d with the binary Q C-LDPC codes constructed by the traditional way, the binary LDPC codes randomly constructed,the 32-ary QC-LDPC codes construct ed based on finite fields and the 64-ary cyclic LDPC codes constructed based on Euclidean geometry ,the NB-LDPC code constructed by the three-dimensional construction can increase 0.56dB,0.56dB, 0.03dB and 0.83dB NCG respectively at the BER of 10－7.Through performan ce simulation of the NB-LDPC code constructed based on this three-dimensional construction,it shows that such an NB-LDPC code not only has quasi-cyclic feat ure,conducive to hardware implementation,but also shows better error corre ction performance in the short code length.