Radiative transitions between charmonium states offer an insight into the internal structure of heavy quark bound states within QCD. In this work, we performed a systematically investigation of the radiative transitions of $$\psi (nS) \rightarrow \gamma \chi _{cJ}(mP)$$ ψ(nS)→γχcJ(mP) and $$\psi (nD) \rightarrow \gamma \chi _{cJ}(mP)$$ ψ(nD)→γχcJ(mP) via intermediate charmed meson loop with a non-relativistic effective field theory. We only focus on the line-shape behavior of the distributions via different intermediate meson loops. Our results show that the coupled-channel effects of these decays are relatively weak, while the coupled channel effects has obvious enhancement when the inial (final) states are closed to the thresholds of charmed-mesons pair.