  We study the effects of vector-like leptons on the $W$ boson mass in a model
with a vector-like $U(1)^\prime$ gauge symmetry. This model provides
simultaneous explanations for the recent anomalies in the muon anomalous
magnetic moment and the semi-leptonic decays of $B$ mesons. We found that the
recent result of the $W$ boson mass precise measurement at CDF can be explained
if the charged (neutral) vector-like lepton is lighter than 250 (80) GeV. The
light vector-like leptons may not be excluded by collider experiments if these
decay to a physical mode of the $U(1)^\prime$ breaking scalar field.
