  In this work, a study of possible molecular states from the
$\Lambda_c\bar{\Lambda}_c$ interaction and their productions in
nucleon-antinucleon collision is performed in a quasipotential Bethe-Salpeter
equation approach. Two bound states with quantum numbers $J^{PC}=0^{-+}$ and
$1^{--}$ are produced with almost the same binding energy from the
$\Lambda_c\bar{\Lambda}_c$ interaction which is described by the light meson
exchanges. However, the result does not support the assignment of
experimentally observed $Y(4630)$ as a $\Lambda_c\bar{\Lambda}_c$ molecular
state because it is hard to obtain a peak near experimental mass of the
$Y(4630)$ which is far above the $\Lambda_c\bar{\Lambda}_c$ threshold. The
possibility to search these states in nucleon-antinucleon collision is studied
by including couplings to $N\bar{N}$ and $D^{(*)}\bar{D}^{(*)}$ channels. The
peaks can be found obviously near the $\Lambda_c\bar{\Lambda}_c$ threshold in
the $D^*\bar{D}^*$ channel at an order of amplitude of 10 $\mu$b. Too small
width of state with $0^{-+}$ may lead to the difficulty to be observed in
experiment. Based on the results in the current work, search for the
$\Lambda_c\bar{\Lambda}_c$ molecular state with $1^{--}$ is suggested in
process $N\bar{N}\to D^*\bar{D}^*$, which is accessible at $\rm \bar{P}ANDA$.
