In this thesis, we study the complex scalar dark matter phenomenology in Gauged Two Higgs Doublet Model (G2HDM). It is shown that a accidental Z 2 symmetry arises naturally from the gauge invariance of SU(2) L ×U(1) Y × SU(2) H ×U(1) X in the model and hence protects the stability of dark matter. The complex scalar dark matter in the model is categorized into inert doublet-like, SU(2) H triplet-like and Goldstone boson-like. While the inert doublet-like dark matter is ruled out by XENON1T data, the SU(2) H triplet-like and Goldstone boson-like dark matter satisfy the relic density from PLANCK and all other experimental constraints from XENON1T, Fermi-LAT and LHC. We discuss in detail the constraints on the parameter space coming from the four pillars of dark matter phenomenology – relic density, direct and indirect detection, and collider searches.