Natural gas is a highly efficient energy source subject to growing demand. Natural gas contains H2S, which can harm human health and cause equipment corrosion and environmental pollution. Effective H2S adsorbents are necessary to overcome these problems. Grand canonical Monte Carlo (GCMS) simulations were performed to study the selectivity and working capacity (pressure swing adsorption (PSA) and vacuum pressure swing adsorption (VSA) processes) of H2S in 33 kinds of stable metal-organic frameworks (MOFs), with the aim of separating H2S from H2S/CH4 gas mixture. ZIF-80, Zn-2-bpydtc, CAU-1-(OH)(2), and CH3O-MOFa were suitable materials for the VSA process. CAU-1-(OH)(2) and CH3O-MOFa were suitable for the PSA process. The structures of materials exhibiting high selectivity and working capacity suggested that appropriate functionality and small pore sizes were important for high selectivity. MOFs with -CI, -OH, and -OCH3 functionality exhibited the strongest adsorption. Materials exhibiting high selectivity, strong interaction with H2S, and large numbers of adsorption sites may have high working capacities. High selectivity and high working capacity stable MOFs were screened and analyzed, to enhance the selectivity and working capacity toward H2S. This provides a theoretical basis for separating H2S from natural gas using MOFs.