Low-density parity-check (LDPC) codes as the best performance of the error control codes, has been widely used in many digital communication standards. Pseudo-Random LDPC is a subclass of LDPC codes, which has been used in space communication technology and Wireless network. A construction method of pseudo-random LDPC code based on finite field is presented in this article, with theoretical analysis and simulation. The construction of pseudo-random LDPC code and the encoding and decoding are studied, and the available decoding algorithm and the quantization scheme are given.