Strongly magnetized and fast-rotating neutron stars are known to be efficient particle accelerators within their magnetosphere and wind. They are suspected to accelerate leptons, protons, and maybe ions to extreme relativistic regimes where the radiation reaction significantly feeds back to their motion. In the vicinity of neutron stars, magnetic field strengths are close to the critical value of B_c ∼ 4.4 · 10^9 T and particle Lorentz factors of the order γ ∼ 10^9 are expected. In this paper, we investigate the acceleration and radiation reaction feedback in the pulsar wind zone where a large-amplitude low-frequency electromagnetic wave is launched starting from the light cylinder. We design a semi-analytical code solving exactly the particle equation of motion including radiation reaction in the Landau–Lifshits approximation for a null-like electromagnetic wave of arbitrary strength parameter and elliptical polarization. Under conventional pulsar conditions, asymptotic Lorentz factor as high as 10^8−10^9 is reached at large distances from the neutron star. However, we demonstrate that in the wind zone, within the spherical wave approximation, radiation reaction feedback remains negligible.