We present a measurement of the W-boson mass using 200 pb{-1} of data collected in pp[over ] collisions at sqrt[s]=1.96 TeV by the CDF II detector at run II of the Fermilab Tevatron. With a sample of 63 964 W-->enu candidates and 51 128 W-->munu candidates, we measure M_{W}=80 413+/-34{stat}+/-34{syst}=80,413+/-48 MeV/c;{2}. This is the most precise single measurement of the W-boson mass to date.