Topological Weyl semimetals (WSMs) have attracted widespread interest due to the chiral Weyl fermions and surface Fermi arcs that enable unique optical and transport phenomena. In this work, we present angle-resolved Raman spectroscopy of TaP, a prototypical noncentrosymmetric WSM, for five excitation wavelengths ranging from 364 to 785 nm. The Raman-active modes, A1, B11, and B12 modes, exhibit two main unique features beyond the conventional Raman theory. First, the relative intensities of Raman-active modes change as a function of the excitation wavelength. Second, angle-resolved polarized Raman spectra show systematic deviation from the Raman tensor theory. In particular, the B11 mode is absent for 633-nm excitation, whereas the B12 mode shows an unusual twofold symmetry instead of a fourfold symmetry for 488-, 532-, and 633-nm excitations. These unconventional phenomena are attributed to the interference effect in the Raman process owing to the existence of multiple carrier pockets with almost the same energy but different symmetries.