We calculated infrared (IR) and Raman spectra of poly(lactic acid) (PLA) polymorphs by employing density functional perturbation theory (DFPT) and a plane wave basis set. Significant different characteristics are found in the calculated spectra of poly(L-lactic acid) (PLLA) alpha-form and PLLA/poly(D-lactic acid) (PDLA) stereocomplex (sc) form. Particularly in the carbonyl stretching region, there is only one sharp peak in the sc-form while there are five peaks in the PLLA alpha-form. A low wavenumber (65 cm(-1)) vibration band of alpha-PLLA observed in a previous terahertz time-domain spectroscopy study was reproduced in the calculated solid-state PLLA spectra. This band could not be obtained by using DFT (B3LYP/6-31G*) simulation on a single PLA oligomer chain and had been attributed to lattice vibrations in the crystal. The permittivity and polarizability tensors of PLA single crystals were also obtained using the DFPT method and were found to be anisotropic.