The vibrationally resolved C 1s single-hole ionization cross sections of H2CO are measured in the region of the σ* shape resonance. The energy of the shape resonance is pushed down by the excitation of the C-O stretching vibration v2′. Our calculations, which take account of elastic multiple scattering within the C-O potential box, show that the downward shift of the shape resonance energy is originated from the elongation of the characteristic internuclear C-O distance in the core-ionized molecule with an increase in v2′. The characteristic internuclear distance varies from R+(0,0,0)=1.198 up to R+(0,2,0)=1.415. In addition to the elastic multiple-scattering mechanism, the internal inelastic scattering of the C 1s photoelectron by valence electrons is suggested as a possible mechanism responsible for the enhancement of vibrational excitations through the shape resonance and near threshold.