  In this paper, the first radial excited heavy pseudoscalar and vector mesons
($\eta_c(2S)$, $\psi(2S)$, $B_c(2S)$, $B^*_c(2S)$, $\eta_b(2S)$,
$\varUpsilon(2S)$) are studied in the Dyson-Schwinger equation and
Bethe-Salpeter equation approach. It is showed that the effective interactions
of the radial excited states are harder than that of the ground states. With
the interaction well determined by fitting the masses and leptonic decay
constants of $\psi(2S)$ and $\varUpsilon(2S)$, the first radial excited heavy
mesons could be quantitatively described in the rainbow ladder approximation.
The masses and leptonic decay constants of $\eta_c(2S)$, $B_c(2S)$, $B^*_c(2S)$
and $\eta_b(2S)$ are predicted.
