We have performed polarized Raman scattering measurements on the newly discovered superconductor Ta4Pd3Te16 (T(c) = 4.6 K). We observe 28 out of 33 Raman active modes, with frequencies in good accordance with first-principles calculations. Although most of the phonons observed vary only slightly with temperature and do not exhibit any asymmetric profile that would suggest strong electron-phonon coupling, the linewidth of the A(g) phonon mode at 89.9 cm(-1) shows an unconventional increase with temperature decreasing, which is possibly due to a charge-density-wave transition or the emergence of charge-density-wave fluctuations below a temperature estimated to fall in the 140-200 K range.