The distribution of dense molecular gas around the supernova remnant G40.5-0.5 has been investigated by radio spectroscopic observations in the CO (J = 1 − 0) transition. The molecular gas is found to extend over the entire region of G40.5-0.5. A molecular shell, with a diameter of ∼ 26 , coincides with the ionized gas as revealed by the cm-radio observations. This coincidence, along with the velocity discontinuity following the shell, provides direct evidence for interaction between the ionized gas and the dense molecular gas. No clear evidence for cosmic-ray acceleration can be identified from this SNR as previously suggested, due to positional uncertainty in relating the SNR shell defined by CO to the EGRET gamma-ray sources, GRO J1904+06, from the gamma-ray observations.