We present a measurement of the ratio of top-quark branching fractions R = B(t --> Wb)/B(t --> Wq), where q can be a b, s, or a d quark, using lepton-plus-jets and dilepton data sets with an integrated luminosity of approximately 162 pb(-1) collected with the Collider Detector at Fermilab during Run II of the Tevatron. The measurement is derived from the relative numbers of tt events with different multiplicity of identified secondary vertices. We set a lower limit of R > 0.61 at 95% confidence level.