  We investigate direct detection rates for Dark Matter candidates arise in a
$SU(2)_L\times U(1)_Y$ with an additional doublet Higgs proposed by Barbieri,
Hall and Rychkov. We refer this model as `Heavy Higgs Model'. The Standard
Model Higgs mass comes out in this model very heavy adopting the few per cent
chance that there is no Higgs boson mass below 200 GeV. The additional Higgs
boson develops neither any VEV due to the choice of coefficient of the scalar
potential of the model nor it has any coupling with fermions due to the
incorporation of a discrete parity symmetry. Thus, the neutral components of
the extra doublet are stable and can be considered as probable candidate of
Cold Dark Matter. We have made calculations for three different types of Dark
Matter experiments, namely, $^{76}$Ge (like GENIUS), DAMA (NaI) and XENON
($^{131}$Xe). Also demonstrated the annual variation of Dark Matter detection
in case of all three detectors considered.
