  A direct WIMP (Weakly Interacting Massive Particle) detector with a neutron
veto system is designed to better reject neutrons. An experimental
configuration is studied in the present paper: a WIMP detectors with CsI(Na)
target is placed inside a reactor neutrino detector. The neutrino detector is
used as a neutron veto device. The neutron background for the experimental
design has been estimated using the Geant4 simulation. The results show that
the neutron background can decrease to O(0.01) events per year per tonne of
CsI(Na). We calculate the sensitivity to spin-independent WIMP-nucleon elastic
scattering. An exposure of one tonne $\times$ year could reach a cross-section
of about 3$\times$$10^{-11}$ pb.
