Grand canonical Monte Carlo method (GCMC) simulation combined with density functional theory calculation was used to investigate the adsorption in Cu-BTC, with nitrogen- and lithium-doping functionalization in order to understand the underlying performance of MOFs in methanol adsorption. A new N-doping structure, 3N–CuBTC, was theoretically constructed by replacing the carbon atoms with hydrogen connection in the organic linkers by nitrogen atoms. 3N–CuBTC shows higher methanol capacity in the measured pressure range due to the increased dispersive interactions caused by the lone electron pair of nitrogen atoms. Another Li-doping structure, 3Li–3N–CuBTC, was fabricated by doping Li atoms on the base of 3N–CuBTC. 3Li–3N–CuBTC demonstrated higher methanol capacity due to the stronger interaction between the induced Li atoms and methanol molecules. Furthermore, these two results can be attributed to the new adsorption sites created by N- and Li-doping, as revealed by the more exothermic binding energies on N-sites (− 49.37 kJ mol−1) and Li-sites (− 122.28 kJ mol−1) than Cu-sites (− 40.62 kJ mol−1). According to the simulation results, it can be concluded that both functionalized Cu-BTCs are capable of enhancing the methanol adsorption capacity of the framework at pressure from 0 to 14 kPa at 298 K.