We report the systematic investigation of the specific heat of the noncentrosymmetric superconductor Li-2(Pd1-xPtx)(3)B as a function of x. There is a large deviation of the phononic specific heat from the conventional Debye specific heat for Pt-rich samples. In contrast with the fully gapped conventional behavior for small x, a power-law temperature dependence of the electronic specific heat is observed even at x = 0.5. These results manifest a strongly anisotropic or nodal superconducting gap even at x = 0.5 and a nodal superconducting gap for x greater than or similar to 0.9.