  We propose a model to explain the W boson mass anomaly reported by the CDFII
collaboration that would suggest new physics (NP). We introduce exotic
fermions; one isospin doublet vector-like lepton, one isospin singlet
singly-charged vector-like lepton, and an isospin doublet inert scalar. The
proposed model provides sizable muon anomalous magnetic moment (muon $g-2$) due
to no chiral suppression and nonzero mass difference between the real and
imaginary parts of neutral inert scalar bosons. The inert scalar mass squared
difference and vector-like exotic leptons ($L', E'$ in the main text) affect
oblique parameters. Especially, the $T$-parameter shift from zero explains the
W boson mass anomaly. We search for the allowed parameter region to explain
both muon $g-2$ and W boson mass anomaly at the same time. We also discuss a
dark matter (DM) candidate assuming the real part of the inert scalar field to
be the one. We find that lighter DM mass is favored to be consistent with
experimental constraints.
