In this paper, we report a molecular simulation study exploring the crystal growth behavior of H2S hydrates within two-phase (H2S hydrate crystal and H,S aqueous solution) and three-phase (H2S hydrate crystal, liquid H2S, and H2S aqueous solution) systems. The microscopic mechanisms of growth, as well as the interfacial properties during the heterogeneous crystal growth process, are probed. We find that the H2S hydrate can be grown at a higher rate than methane hydrates under comparable conditions (Vatamanu, J.; Kusalik, P. G. J. Phys. Chem. B 2006,110, 15896). The three-phase simulations, which also allow us to identify the simulation conditions on the experimental phase diagram, demonstrate that the present models reasonably reproduce the phase behavior of this system. We find that the crystal interface has a strong affinity for water molecules. We observed a relatively low level of defects in the newly formed H2S hydrate crystal.