In this work, the adsorptions of carbon dioxide, methane, nitrogen, and hydrogen sulfide and the separation of their binary mixtures into NUM-3a Metal-Organic Framework (MOF) were studied through Grand Canonical Monte Carlo (GCMC) simulation method. The simulated pure gas uptakes using three generic force fields (UFF, Dreiding, and OPLS) at 298 K were compared with the experimental values. The accuracy of the applied force fields for each gas was compared with the experimental isotherms and discussed. Our results show that OPLS has the best accuracy in the case of methane while Dreiding was the best for CO2 and N2. Simulated gas uptakes indicated that H2S was more adsorbed by NUM-3a than CO2, CH4, and N2. The calculated adsorption selectivity of NUM-3a for the binary mixtures of CH4 with H2S is larger than that of CO2. NUM-3a possess more affinity for H2S and CO2 than for CH4, where it may be a promising adsorbent material for separating carbon dioxide and hydrogen sulfide from methane. Furthermore, the most probable sites for the adsorption of the studied gases on the NUM-3a were investigated. The heats of adsorptions, as well as Henry’s law constants, were also calculated, and it was in line with the observed gas adsorptions. The most preferred sites for the adsorption of carbon dioxide and hydrogen sulfide are the carboxyl groups and inside the channels and around the metal centers. However, methane and nitrogen are mainly accumulating in the channels’ s apexes of NUM-3a around the metal center.