Density functional theory (DFT) computations have been carried out to study the structure and stability of MoSx clusters with the change of sulfur coverage at both Mo and S edges. DFT shows that adding sulfur to the Mo edge is always exothermic. However, deleting corner sulfur from the S edge is exothermic for 67 and 50% sulfur coverages, while deleting edge sulfur from the S edge is endothermic for 33 and 0% sulfur coverages. On the basis of the computed free energies along a wide range of H2S/H-2 ratios, it is found that there are two stable structures with 33 and 50% sulfur coverages on the Mo edge by having 100% sulfur coverage on the S edge and one stable structure with 67% sulfur coverage on the S edge by having 0% sulfur coverage on the Mo edge. Under fully sulfiding atmosphere or at a very high H2S/H-2 ratio, triangle MoSx, structures with 100% sulfur coverage on the Mo edge are computed to be more stable than those with 100% sulfur coverage on the S edge, in agreement with the observation of scanning tunneling microscopy. In addition, the effects of cluster sizes on the surface structures are discussed.