Positron affinities (PAs), which is the binding energy of a positron, of hydrogen cyanide (HCN) and formaldehyde (CH2O) molecules at vibrational excited states were theoretically analyzed with both the multi-component molecular orbital and vibrational quantum Monte Carlo methods, in order to elucidate the effect of molecular vibrations on the binding of a positron to the molecules. For HCN molecule, we found that the vibrational excitations of the CN and CH stretching modes enhance PA values in comparison to the value at the ground state, whereas the excitation of bending mode deenhances it. For CH2O molecule, the vibrational excitation of C=0 stretching mode gives the largest contribution to the PA enhancement among all vibrational modes. Using the linear regression analysis, we confirmed that the PA variations at each vibrational state mainly arise from the changes in the permanent dipole moment by vibrational excitations.