Slurry bed hydrotreating process can treat inferior heavy oil and residual oil from different sources. Therefore, compared with other processes, the process is characterized by strong adaptability of raw materials. One of the main reactions of heavy oil hydrotreating is the activation of hydrogen. Molybdenum-based dispersed catalyst is widely used as an efficient hydrogenation catalyst in the slurry bed hydrogenation process. One of the key factors affecting the hydrogenation activity of heavy oil is the dispersion of molybdenum-based catalysts. Therefore, it is meaningful to explore the dispersion of the catalyst for hydrogen activation. In this paper, Mo7S15, Mo12S26, Mo18S39, Mo25S54 and Mo33S71 clusters were built and their structure is optimized. On the basis of stable structure, the stability and activity of clusters with different sizes were studied, and the adsorption dissociation process of hydrogen on Mo x S y clusters with different sizes was discussed, including the stability of hydrogen molecules at different adsorption sites, the adsorption dissociation process of hydrogen molecules on Mo x S y clusters with different sizes, and the changes with the size of Mo x S y clusters. According to the calculation results, it is found that the currently established clusters with smaller size have the lower binding energy, the smaller HOMO-LUMO energy gap value, the weaker stability and the stronger activity. During the adsorption and dissociation of H2 above the cluster, it is found that hydrogen is more easily adsorbed at the edge position. With the increase of cluster size, the adsorption energy was -64.25, -34.60, -34.14, -7.20 and -6.82 kJ/mol; the absolute value of the adsorption energy decreased; the interaction between hydrogen molecules and the cluster was weaker; the dissociation energy gradually increased, and were 13.76, 33.14, 53.64, 60.75 and 64.47 kJ/mol, respectively. The current results show that the smaller the cluster size, the easier it is for hydrogen to adsorb/ dissociate and the cluster shows higher activity.