  The deviations of the recent measurements of the muon magnetic moment and the
$W-$boson mass from their SM predictions hint to new physics beyond the SM. In
this article, we address the observed discrepancies in the $W$-boson mass and
muon anomalous magnetic moment in the Inert Two Higgs Doublet Model (I2HDM)
extended by a complex scalar field singlet under the SM gauge group. The model
is constrained from the existing LEP data and the measurements of partial decay
widths to gauge bosons at LHC. It is shown that a large subset of this
constrained parameter space of the model can simultaneously accommodate the
$W$-boson mass and also explain the muon $g-2$ anomaly.
