Light hydrocarbon gases, such as methane, ethane, propane, ethylene, and propene, are commonly used in manufacturing processes as raw material or energy fuel. Traditionally, these gases are mainly separated by cryogenic distillation, which requires massive amounts of energy because of high-pressure and low-temperature operating conditions. Many studies have shown that metal–organic frameworks (MOFs) are potential materials for gas storage and separation because of their unique properties, such as high surface area, nontoxicity, and large gas storage capacity. UiO-66 and its modified materials are considered ideal candidates for gas storage and separation and have attracted increased attention since they can be easily synthesized and are thermally and chemically stable. In this study, we used grand canonical Monte Carlo (GCMC) to simulate and understand the gas adsorption behaviour of UiO-66 and its variants, including UiO-66-NO2, UiO-66-NH2, UiO-66-Br, and UiO-66-(CH3)2, for pure light hydrocarbon gases and their binary mixtures. The adsorption isotherm and adsorption site energy distribution are analysed and discussed to identify the best candidate for gas adsorption and separation. It is found that the modified form of UiO-66-NH2 has good selectivity, large gas storage potential, and high working capacity compared to UiO-66. Further insight into favourable gas adsorption positions is discussed.