We present a measurement of the $W$-boson mass, $M_W$, using data corresponding to 2.2/fb of integrated luminosity collected in ppbar collisions at $sqrt{s}$ = 1.96 TeV with the CDF II detector at the Fermilab Tevatron. The selected sample of 470126 $Wto e u$ candidates and 624708 $Wtomu u$ candidates yields the measurement $M_W = 80387pm 12$ (stat) $pm 15$ (syst)$ = 80387 pm 19$ MeV$/c^2$ . This is the most precise single measurement of the $W$-boson mass to date.