A novel construction method with grith-8 quasi-cyclic low-density parity-check (QC-LDPC) codes based on the Golomb ruler is proposed to solve the issue of short-cycle structures affecting error-correction performance. First, a set is constructed by selecting some elements from the Golomb ruler based on the code-length and code-rate requirements. Subsequently, by combining the girth-4 and girth-6 properties of the elemental locations in the exponential matrix, another set is obtained using the search algorithm to search for elements that satisfy the conditions of no girth-4 and no girth-6. Subsequently, the corresponding exponential matrix is constructed. Finally, a parity-check matrix is obtained. Simulation results show that the net coding gain of the GR-QC-LDPC code constructed using the proposed method is greater than those yielded by four other QC-LDPC codes with the same code-rate and code-length at a bit error rate of 10^-6; moreover, its error floor is insignificant.