A direct measurement of the total decay width of the W boson Gamma(W) is presented using 350 pb(-1) of data from pp[over ] collisions at square root 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 enu and micronu in the transverse-mass region 50<M(T)<90 GeV and then fitting the predicted shape to 6055 events in the high-M(T) region, 90<M(T)<200 GeV. The result is Gamma(W)=2032 +/- 45(stat)+/-57(syst) MeV, consistent with the standard model expectation.