Abstract The surface structure of Au-adsorbed Si(111)-5 × 2 with short-range order has been observed through STM measurements. Particularly, the one-dimensional chains consisting of adsorbed Au atoms are clearly observed. A one-dimensional lattice model is constructed for this chain, with repulsive interactions and some assumed irregularity corresponding to STM observation. The theoretical positional correlation function of the adsorbed Au is obtained by a Monte Carlo simulation with fitting parameters of the repulsive interaction and of the irregularity of the experimental positional correlation function. Almost complete fitting is obtained, from which reasonable values of the repulsive interaction and concentration of the irregularity are obtained. A rigorous analysis is also made of another one-dimensional model to describe the inter-chain correlation on this surface, and is compared with experimental findings.