We introduce a two-phase xenon detector, and its detection mechanism, for detecting WIMP (weakly interactive massive particle) dark matter directly. The two-phase xenon detector provides an outstanding method for discriminating a MIP (minimum ionization particle)-type, for example gamma-ray, background from a WIMP signal. The two-phase xenon detector produces primary scintillation and a secondary signal simultaneously. The ratio between the primary and the secondary signal play a key role in identifying the WIMP signal and the MIP-type background. The secondary signal is too weak to discriminate it from the background easily for our xenon detector. Here, we introduce a secondary signal amplification method using electroluminescence in liquid xenon. Using that method, we achieved a 4.3 x 10 +/- 4.9 times larger amplification ratio for the secondary signal in the liquid xenon, which will increase the efficiency of the two-phase xenon detector to search for super-symmetric dark matter, WIMP.