We obtain a closed expression for the response function for damped anharmonic vibrational modes using the Feynman rule obtained through the nonequilibrium generating functional derived in our previous paper [Phys. Rev. E 53, 214 (1996)]. The linear absorption spectra are explicitly calculated through the Feynman diagrams for molecules with anharmonic potential in solution, The dependence of the spectra both on the temperature and on the solvent nature can be taken into account in our theory. The result is examined numerically for various dampings, anharmonicities, and temperatures.