  We consider a particle dark matter model by extending the scalar sector of
the Standard Model by an additional SU(2) scalar doublet which is made "inert"
(and stable) by imposing a discrete $Z_2$ symmetry under which the additional
scalar doublet is odd (and the SM is even) and it does not develop any vacuum
expectation value (VEV). The lightest inert particle (LIP) of this inert
doublet model (IDM) can be a viable candidate for Dark Matter. The IDM model is
further extended by an additional singlet scalar which is also even under $Z_2$
and develop a VEV on spontaneous symmetry breaking. This additional scalar
singlet mixes with SM Higgs and on diagonalisation of the mass matrix two CP
even scalar eigenstates are obtained one of which is attributed to the physical
Higgs (with mass 125.09 GeV). The LIP is the dark matter candidate in the
extended model. For such a particle dark matter model we explore the
first-order electroweak phase transition and the consequent production of
Gravitational Waves (GW) at that epoch of the early Universe and calculate the
intensities and frequencies for such waves. We then investigate the detection
possibilities of such GWs at the future spaceborne primordial GW detectors such
as eLISA, BBO, ALIA, DECIGO, U-DECIGO and ground-based detector aLIGO.
