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. This 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 mass measurement on the parameter space. We impose other constraints, including theoretical requirements, flavor-changing neutral currents in physics, the cutoff scale above 1 TeV, Higgs precision data, and direct collider search limits from the LEP, Tevatron, and LHC experiments. We find that upper bounds exist on the masses of the heavy Higgs bosons. And type-II and type-Y in the inverted scenario are completely excluded. Simultaneous explanation including the muon g-2 is also discussed in the Higgs-phobic type-X.