  A new type of neutron detector, named Stack Structure Solid organic
Scintillator (S$^4$), consisting of multi-layer plastic scintillators with
capability to suppress low-energy $\gamma$ rays under high-counting rate has
been constructed and tested. To achieve $\it{n}$-$\gamma$ discrimination, we
exploit the difference in the ranges of the secondary charged particles
produced by the interactions of neutrons and $\gamma$ rays in the scintillator
material. The thickness of a plastic scintillator layer was determined based on
the results of Monte Carlo simulations using the Geant4 toolkit. With layer
thicknesses of 5 mm, we have achieved a good separation between neutrons and
$\gamma$ rays at 5 MeV$_{\rm ee}$ threshold setting. We have also determined
the detection efficiencies using monoenergetic neutrons at two energies
produced by the $\it{d}$+$\it{d}\to\it{n}$+$^{3}$He reaction. The results agree
well with the Geant4 simulations implementing the Li$\grave{\rm e}$ge
Intranuclear Cascade hadronic model (INCL++) and the high-precision model of
low-energy neutron interactions (NeutronHP).
