We investigate direct detection rates for Dark Matter candidates arise in a SU (2)L× U (1)Y with an additional doublet Higgs proposed by Barbieri, Hall and Rychkov. We refer to this model as "Heavy Higgs Model". The Standard Model Higgs mass comes out from this model is very heavy, so there is very slim 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
Dark-matter pair production at the ILC in the littlest Higgs model with
T
-parity
