The compound [34](1,2,4,5)cyclophane, which consists of π-stacked two benzene rings, is one of the simplest dimeric molecules with a transannular π-π interaction. Its radical cation showed a characteristic near-infrared electronic absorption due to a transition from "bonding" to "anti-bonding" orbitals between the two benzene moieties. The Raman spectrum was measured in resonance with this electronic transition, and selective enhancement of low-frequency vibrational bands was observed. The strongest band at 241 cm-1 was assigned to one of the inter-ring vibrations that changed the distance between the two benzene rings. The Raman cross-section of this band was estimated to be 9.1 × 10-25 cm-2, which was comparable to typical resonance Raman cross-sections and 100 times stronger than those of the local ring-breathing vibrations (1230 and 1262 cm-1) of the radical cation. To understand this resonance Raman enhancement, the polarized Raman spectra were measured. The depolarization ratios of the cation bands were almost 1/3, which indicates an A-term rigorous resonance Raman effect with a contribution of a single electronic excited state. To analyze this A-term resonance Raman effect, the optimized geometry was calculated for the electronic excited S2 state of the radical cation responsible for its near-infrared electronic absorption. The bond lengths of the excited S2 state were almost the same as those of the ground state, while the distance between the two benzene rings extended by 7%. Large Franck-Condon factors were, thus, expected for the inter-ring vibrations, and resulted in the selective resonance Raman enhancement of these large amplitude vibrations.