  We investigate the charmed baryon production reaction
$p\bar{p}\rightarrow\Lambda_c\bar{\Lambda}_c$ in an effective Lagrangian
approach. Besides the $t$-channel $D^0$ and $D^{*0}$ mesons exchanges, the
$s$-channel $Y(4630)$ meson exchange is taken into account. For the total cross
sections, the $D^0$ and $D^{*0}$ mesons provide minor background contributions,
while the $Y(4630)$ state gives a clear peak structure with the magnitude of 10
$\mu$b at center of mass energy 4.63 GeV. Basing on the results, we suggest
that the reaction of $p\bar{p}\rightarrow\Lambda_c\bar{\Lambda}_c$ can be used
to search for the $1^{--}$ charmonium-like $Y(4630)$ state, and our predictions
can be tested in future by the $\rm{\bar PANDA}$ facility.
