A direct WIMP ( Weakly Interacting Massive Particle ) detector with a neutron veto system is designed to better reject neutrons .
Two experimental configurations are studied in the present paper : one is for an Xe detector enclosed in a Gd-loaded scintillator and the other one is for an Xe detector placed inside a reactor neutrino detector .
The Gd-doped liquid scintillator ( or the neutrino detector ) is used as a neutron veto device .
The neutron backgrounds for the two experimental designs have been estimated using Geant4 simulations .
The results show that the neutron backgrounds can decrease to O ( 0.1 ) events per year per tonne of liquid Xenon .
We calculate the sensitivities to spin-independent WIMP-nucleon elastic scattering .
An exposure of one tonne \times year could reach a cross-section of about 6 \times 10 ^ { -11 } pb .