  Very recently, the LHCb collaboration released the newest measurements of
$B_s \to J/\psi p\bar{p}$, where an enhancement structure near 4.34 GeV was
observed in the invariant mass spectrum of $J/\psi p$ with the statistical
significance of $3.1-3.7$ $\sigma$. In this work, by performing a combined
analysis for the three invariant mass spectra of $B_s \to J/\psi p\bar{p}$, we
find that this $J/\psi p$ structure near 4.34 GeV can correspond to the
contributions from the $P_c(4380)^+$ state with the assumption of
$J^{P}=3/2^{-}$ together with the reflections of $B_s \to (f_2^{*} \to
p\bar{p})J/\psi$. Here, $P_c(4380)$ was first observed in $\Lambda_b \to J/\psi
p K$ but not confirmed in the updated LHCb data in 2019, and $f_2^{*}$ means
the exciting light isoscalar tensor meson around 2.0 GeV. Thus, this provides a
possible evidence to support the existence of the pentaquark $P_c(4380)$.
Specifically, the assumed spin parity $J^{P}=3/2^{-}$ of $P_c(4380)$ is
consistent with a prediction of the theoretical explanation of an $S$-wave
$\bar{D}\Sigma_c^*$ molecular bound state.
