We present a measurement of the fractions F0 and F+ of longitudinally polarized and right-handed W bosons in top-quark decays using data collected with the CDF II detector. The data set used in the analysis corresponds to an integrated luminosity of approximately 318  pb−1. We select tt candidate events with one lepton, at least four jets, and missing transverse energy. Our helicity measurement uses the decay angle θ∗, which is defined as the angle between the momentum of the charged lepton in the W boson rest frame and the W momentum in the top-quark rest frame. The cosθ* distribution in the data is determined by full kinematic reconstruction of the tt candidates. We find F0=0.85+0.15−0.22(stat)±0.06(syst) and F+=0.05+0.11−0.05(stat)±0.03(syst), which is consistent with the standard model prediction. We set an upper limit on the fraction of right-handed W bosons of F+<0.26 at the 95% confidence level.