Molybdenum disulfide (MoS2) nanoclusters have recently attracted enormous interest, due to their promising applications as catalysts in hydrodesulfurization of fossil fuels. It has been demonstrated that the catalytic activity of MoS2 nanoclusters closely relates to their equilibrium morphology, which is in turn quite sensitive to various, factors, such as the synthesis environments, the cluster size, and the substrates. Here, we carry out the density functional theory (DFT) calculations to study the size dependent morphology change of triangular MoS2 nanoclusters with all these factors systematically considered. Our results indicate that the stability of triangular MoS2 nanoclusters is mainly determined by their edge and corner energies, and the variation of the ratio of the edge to corner energies with respect to the cluster size, chemical potential of sulfur, and substrates could induce a structural transition for their equilibrium morphology. By setting the chemical potential to fit experimental conditions, our calculations reveal a size-dependent morphology transition of triangular MoS2 nanoclusters on Au(111) substrate, which is quantitatively consistent with experiments. In addition, the electronic structures of triangular MoS2 nanoclusters are carefully studied. The results indicate that the metallic edge states, which is important for the hydrodesulfurization catalysis, are very sensitive to the substrates and only the clusters with Mo edge on Au(111) is found to have the one-dimensional metallic edge states. This result implies that in addition to the Mo edge, the metallic substrates may also play an important, role in understanding the experimentally observed catalytic activity of MoS2 nanoclusters, which has never been considered before.