A direct measurement of the total decay width of the W boson ΓW is presented using 350  pb−1 of data from pp¯ collisions at s√=1.96  TeV collected with the CDF II detector at the Fermilab Tevatron. The width is determined by normalizing predicted signal and background distributions to 230 185 W candidates decaying to eν and μν in the transverse-mass region 50<90  GeV and then fitting the predicted shape to 6055 events in the high-MT region, 90<200  GeV. The result is ΓW=2032±45stat±57syst  MeV, consistent with the standard model expectation.