In this work, the adsorption of acetylene and its binary mixture with methane on MOF-5, HKUST-1 and MOF-505 was studied using Grand Canonical Monte Carlo molecular simulations. The preferred adsorption sites of acetylene and methane molecules into metal–organic frameworks (MOFs) were investigated. The simulated adsorption isotherms of acetylene on MOF-5 and MOF-505 agreed well with the experimental ones without any reparameterisation of the potential parameters but for HKUST-1 the interaction parameters of the acetylene and copper ion were reparameterised. Comparisons of the calculated adsorption isotherms of acetylene in the studied MOFs showed that the MOF-5 had the lowest adsorption capacity. Our results revealed that guest molecules were most adsorbed on the entrance windows of the octagon pore of HKUST-1, while the preferred adsorption sites were large pores and on the metal ion cluster of MOF-505 and MOF-5, respectively. Adsorption of binary mixtures of methane and acetylene on MOF-5, HKUST-1 and MOF-505 revealed that acetylene adsorption is higher than that of methane. Finally, the results showed that C2H2/CH4 selectivity values on HKUST-1 are significantly higher than on MOF-505 and MOF-5. The preferred adsorption sites of acetylene and methane in an equimolar binary mixture were calculated and discussed.