This Letter describes a direct measurement of the W boson total decay width, gamma(W), using the Collider Detector at Fermilab. The measurement uses an integrated luminosity of 90 pb(-1), collected during the 1994-1995 run of the Fermilab Tevatron p&pmacr; collider. The width is determined by normalizing predicted signal and background distributions to 49 844 W-->enu candidates and 21 806 W-->&mgr;nu candidates in the transverse-mass region M(T)<200 GeV and then fitting the predicted shape to the 438 electron events and 196 muon events in the high- M(T) region, 100<M(T)<200 GeV. The result is gamma(W) = 2.04+/-0.11(stat)+/-0.09(syst) GeV.