  With regard to the leptonic magnetic dipole moment anomaly as well as the
$W$-boson mass excess, we study the DFSZ axion model. Considering theoretical
and experimental constraints, we show that the muon and electron $g-2$
anomalies can be explained within the parameter space of the model for extra
Higgs bosons with mass spectra around the electroweak scale and for an almost
equivalent contribution of one- and two-loop diagrams. A negative electron
$g-2$ could be achieved by introducing heavy neutrinos. Furthermore, the $W$
boson mass excess can be consistently addressed within the mass range of the
matter content testable at collider experiments.
