The predicted neutrinoless double-β (0vββ) decay is the crucial phenomenon to prove the existence of the Majorana neutrino, which gives a foundation to leptogenesis to explain the matter prevalence of the universe. The nuclear matrix element (NME) of 0vββ decay is an important theoretical quantity to determine the effective neutrino mass and help the detector design for the next generation of the 0vββ decay search. Reliable calculation of this NME is a long-standing problem because of the diversity of the predicted values of the NME. The main reason for this difficulty is that the effective strength of the Gamow-Teller transition operator $g_A$ for this decay is unknown. I will show the lowest-order vertex corrections for the 0vββ and the 2vββ NME of 136Xe in the framework of the hybrid application of the quantum field theory to the leptons and the Rayleigh-Schrödinger perturbation to the nucleus. The unperturbed nuclear states are obtained by the quasiparticle random-phase approximation. These corrections reduce the 0vββ NME by 30%. The effective $g_A$ referring to this reduced NME is also obtained, and it is shown for the first time that the effective $g_A$ for the 0vββ NME is not quite different from that for the 2vββ NME; the difference is only 10%.