Complexes of dimethyl sulfoxide with F-, Cl-, OH-, CH3O-, HCOO-, and NO2- anions were studied at MP2/6-31+G* and B3LYP/6-31+G* levels of theory. The energies, geometries, NBO charges, and topological charge densities were analyzed. The formation of bidentate hydrogen-bonded complexes was verified. The combined hydrogen bonding and electrostatic charge-dipole interaction was proposed to be the base of complex formation.