Density functional theory method was applied to investigate adsorption of thiophene, benzene, and hexane in Na-, Ag-, and Cu-exchanged mordenite (MOR). A cluster model containing 16 tetrahedral atoms was constructed as structure model of MOR. The charge-balancing metallic ions (Na+, Ag+, and Cu+) were introduced to produce the Lewis acid site (LAS). The acidic strength was estimated by calculating adsorption energy of NH3 in the model. The equilibrium configurations, Mulliken charge populations, and adsorption energies of thiophene, benzene, and hexane in models were calculated and analyzed. For the adsorbates investigated, interaction strengths followed the decreasing order of Cu–MOR > Ag–MOR > Na–MOR that agreed well with their Lewis acidic strengths. The interaction strengths followed the order of thiophene ≈ benzene > hexane in Na–MOR, and thiophene > benzene > hexane in Cu–MOR and Ag–MOR. Moreover, the interaction mechanisms of thiophene and benzene in Cu–MOR and Ag–MOR were investigated by the natural bond orbital (NBO) analysis. Furthermore, similar calculations were carried out for the adsorption of thiophene, benzene, and hexane in the naked Na+, Cu+, and Ag+ for comparison.