We calculated transitions of the higher radial excited charmonia $$ \psi (nS) ~ ( n=3,4,5 )$$ $\psi \left(nS\right)(n=3,4,5)$ to the orbital excited charmonium $$ h_c(1P) $$ $h_c\left(1P\right)$ with emission of one pion or eta meson. In calculations, the intermediate S- and P-wave charmed meson loops were considered in terms of the nonrelativistic effective field theory. The results indicate that the transitions of interest are dominated by the loops involving the $$ s_l^P=(1/2)^+ $$ $s_l^P={(1/2)}^{+}$ charmed mesons, whereas the $$ s_l^P=(1/2)^- $$ $s_l^P={(1/2)}^{-}$ charmed meson loops are of minor contributions. The partial decay widths of $$ \psi (nS) \rightarrow h_c \pi ^0 $$ $\psi \left(nS\right)\to h_c{\pi }^0$ are of the order of 0.01–1 keV. For the case of $$ \psi (nS) \rightarrow h_c \eta $$ $\psi \left(nS\right)\to h_c\eta$ , the partial decay widths are from 0.1 to 100 keV, implying the branching ratios from $$ 10^{-5} $$ ${10}^{-5}$ to $$ 10^{-3} $$ ${10}^{-3}$ . Moreover, the partial decay widths for $$ \psi (nS) \rightarrow h_c \eta $$ $\psi \left(nS\right)\to h_c\eta$ are found to decrease as the $$ \eta $$ $\eta$ - $$ \eta ' $$ ${\eta }^{\prime }$ mixing angle increases. It is hoped that the present calculated results would be observed in the future experiments.