  The most recent $W$-boson mass measurement by the CDF collaboration with a
substantially reduced uncertainty indicates a significant deviation from the
standard model prediction, as large as $7\sigma$ if taken literally. Then the
Peskin-Takeuchi parameters of $S$ and $T$ shift to larger values, which has
profound consequences in searching for physics beyond the SM. In the framework
of two-Higgs-doublet models, we study the effect of the new $W$-boson mass
measurement on the parameter space. Combined with other constraints including
theoretical requirements, flavor-changing neutral currents in $B$ physics, the
cutoff scale above 1 TeV, Higgs precision data, and direct collider search
limits from the LEP, Tevatron, and LHC experiments, we find upper bounds on the
masses of the heavy Higgs bosons: $M_{H, A, H^\pm} \lesssim 1.1$ TeV in type I,
II, X, and Y for the normal Higgs scenario; $M_{H^\pm} \lesssim 450 $ GeV and
$M_{A} \lesssim 420 $ GeV in type I and X for the inverted scenario where the
heavier $CP$-even Higgs boson is the observed one. Another important finding is
that type II and type Y in the inverted scenario are completely excluded. Such
unprecedented findings imply that the upcoming LHC run can readily close out a
large portion of the still-available parameter space.
