  We investigate the neutral hidden charm pentaquark states $P_c^0(4380)$ and
$P_c^0(4450)$ in $\pi^-p \to J/\psi n$ reaction within an effective Lagrangian
approach. The background contributions for the process mainly come from
$t$-channel $\pi$ and $\rho$ meson exchanges. The contributions of
$P_c^0(4380)$ and $P_c^0(4450)$ states give clear peak structures in the
magnitude of 1 $\mu$b at center of mass energy 4.38 GeV and 4.45 GeV in the
total cross sections. Hence, this reaction may provide a new good platform to
search for neutral $P_c$ states. It is expected that our estimated total cross
sections together with the angular distributions can be tested by future
experiments at J-PARC.
