  The new CDF II measurement of $W$-boson mass shows a 7$\sigma$ deviation from
the Standard Model (SM) prediction, while the recent FNAL measurement of the
muon $g-2$ shows a 4.2$\sigma$ deviation (combined with the BNL result) from
the SM. Both of them strongly indicate new physics beyond the SM. In this work
we study the implication of both measurements on low energy supersymmetry. With
an extensive exploration of the parameter space of the minimal supersymmetric
standard model (MSSM), we find that in the parameter space allowed by current
experimental constraints from colliders and dark matter detections, the MSSM
can simultaneously explain both measurements on the edge of $2\sigma$ level,
taking theoretical uncertainties into consideration. The favored parameter
space, characterized by a compressed spectrum between bino, wino and stau, with
the stop being around 1 TeV, may be covered in the near future LHC searches.
