We carried out measurements of the magnetoresistance, magnetic susceptibility and specific heat on crystals of the low-dimensional transition metal telluride Ta4Pd3Te16. Our results indicate that Ta4Pd3Te16 is an anisotropic type-II superconductor in the clean limit with the extracted Ginzburg-Landau parameter KGL = 84. The upper critical field Hc2(T) shows an anomalous temperature dependence at low temperatures and the anisotropy of Hc2(T) is strongly T-dependent, both of which indicate a multiband scenario. The electronic specific heat Cel(T) can be consistently described by a two-gap (s + d waves) model from the base temperature T/Tc ~ 0.12 up to Tc. Our results suggest nodal and multiband superconductivity in Ta4Pd3Te16.