Functionalization of metal-organic framework (MOF) ligands can tune the adsorption properties of MOFs. The adsorptions of NO, NO2, NH3, C5H5N, C4H5N, and C4H4O on pristine and five X-functionalized HKUST-1, i.e. Cu3(BTC)2 (BTC = 1,3,5-benzenetricarboxylate) (X = CH3, CH3O, NH2, NO2, and Br) are evaluated by van der Waals corrected density functional theory calculations. Despite the fact that the open metal center is the energetically preferred adsorption site for most of them, the functional group site can yield a comparable adsorption ability with the open metal center. This is particularly true for pyrrole C4H5N adsorption on CH3O-functionalized HKUST-1 where the functional group site shows stronger adsorption stability than the open metal center site, probably due to the formed hydrogen bond between pyrrole and the CH3O functional group. While the CH3- or CH3O-functionalized organic linker in these MOFs strengthens the adsorption of all the considered species, that of NO2-, Br-, or NH2-functional groups reduces, which is associated with their topologies. Among them, only CH3- or CH3O-functionalized HKUST-1 presents the fmj (orthorhombic crystal system) topology while all the others are isostructural to the pristine HKUST-1 with the tbo (twisted boracite-type, cubic) topological structure. Among six adsorbates, two basic adsorbates, C5H5N and NH3, always yield the strongest bonding strength upon adsorption on the pristine and five functionalized HKUST-1. Electronic properties including the Bader charges, electron density differences, and electron localization function were investigated to comprehend their adsorption behaviors. This work provides guidance for the proper functionalization of HKUST-1 with improved adsorption properties for specific adsorbates.