Density functional theory calculations were used to analyze the interactions in 1 : 1 and 1 : 2 complexes of naphthalene (NAP) with dimethyl ether (DME). The structures of complexes have been determined using M05-2X density functional and the aug-cc-pVDZ basis set. The structures obtained were analyzed with the quantum theory of atoms in molecules (QTAIM), the energy decomposition analysis, and many-body interaction energies methodologies. Two minima were located on the potential energy surface of the 1 : 1 complexes. Four different structures have been obtained for the 1 : 2 complexes. Two types of interactions are observed, CH⋯O and CH⋯π hydrogen bonds. Interaction energies of the 1 : 1 and 1 : 2 complexes are in the range 9–12 kJ mol–1 and 20–27 kJ mol–1, respectively, at the M05-2x/aug-cc-pVDZ level of theory.