This paper describes a measurement of the top quark mass, Mtop, with the dynamical likelihood method (DLM) using the CDF II detector at the Fermilab Tevatron. The Tevatron produces top/antitop (tt) pairs in pp collisions at a center-of-mass energy of 1.96 TeV. The data sample used in this analysis was accumulated from March 2002 through August 2004, which corresponds to an integrated luminosity of 318  pb−1. We use the tt candidates in the “lepton+jets” decay channel, requiring at least one jet identified as a b quark by finding a displaced secondary vertex. The DLM defines a likelihood for each event based on the differential cross section as a function of Mtop per unit phase space volume of the final partons, multiplied by the transfer functions from jet to parton energies. The method takes into account all possible jet combinations in an event, and the likelihood is multiplied event by event to derive the top quark mass by the maximum likelihood method. Using 63 tt candidates observed in the data, with 9.2 events expected from background, we measure the top quark mass to be 173.2+2.6−2.4(stat.)±3.2(syst.)  GeV/c2, or 173.2+4.1−4.0  GeV/c2.