The quantum mechanics (QM) method and Grand Canonical Monte Carlo (GCMC) simulations were performed to study the effect of lithium cation doping on the adsorption and separation of CO2, CH4 and H2 on 2-fold interwoven metal-organic framework (MOF) Zn2(NDC)2(diPyNI). The second order Moller-Plesset (MP2) calculations on the (Li+-diPyNI) cluster model showed that the energetically most favorable lithium binding site is above the pyridine ring side and at a distance of 1.82 Å from the oxygen atom. The results revealed that the adsorption capacity of Zn2(NDC)2(diPyNI) for carbon dioxide is higher than that of hydrogen and methane at room temperature. Furthermore, the GCMC simulations on the obtained structures from QM calculations predicted that the Li+-doped MOF had higher adsorption capacities than the nondoped MOF, especially at low pressures. In addition, the probability density distribution plots displayed that CO2, CH4 and H2 molecules accumulate close to the Li cation site. The selectivity results indicated that CO2/H2 selectivity values in Zn2(NDC)2(diPyNI) was higher than those of CO2/CH4. The selectivity of CO2 over CH4 on Li+-doped Zn2(NDC)2(diPyNI) is relatively improved compared to the undoped MOF.