A measurement of the top-quark mass is presented using Tevatron data from proton-antiproton collisions at center-of-mass energy s√=1.96  TeV collected with the CDF II detector. Events are selected from a sample of candidates for production of tt pairs that decay into the lepton + jets channel. The top-quark mass is measured with an unbinned maximum likelihood method where the event probability density functions are calculated using signal and background matrix elements, as well as a set of parametrized jet-to-parton transfer functions. The likelihood function is maximized with respect to the top-quark mass, the signal fraction in the sample, and a correction to the jet energy scale (JES) calibration of the calorimeter jets. The simultaneous measurement of the JES correction (ΔJES) amounts to an additional in situ jet energy calibration based on the known mass of the hadronically decaying W boson. Using the data sample of 578 lepton+jets candidate events, corresponding to 3.2  fb−1 of integrated luminosity, the top-quark mass is measured to be mt=172.4±1.4(stat+ΔJES)±1.3(syst)  GeV/c2.