We present a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element vertical bar V-cb vertical bar using the decay B -> Dl nu(l) (l = e,mu) based on 711 fb(-1) of e(+)e(-) -> Upsilon(4S) data recorded by the Belle detector and containing 772 x 10(6) B (B) over bar pairs. One B meson in the event is fully reconstructed in a hadronic decay mode, while the other, on the signal side, is partially reconstructed from a charged lepton and either a D+ or D-0 meson in a total of 23 hadronic decay modes. The isospin-averaged branching fraction of the decay B -> Dl nu(l) is found to be B(B-0 -> D(-)l(vertical bar)nu(l)) = (2.31 +/- 0.03(stat) +/- 0.11(syst))%. Analyzing the differential decay rate as a function of the hadronic recoil with the parametrization of Caprini, Lellouch, and Neubert and using the form-factor prediction G(1) = 1.0541 +/- 0.0083 calculated by FNAL/MILC, we obtain eta(EW)vertical bar V-cb vertical bar = (40.12 +/- 1.34) x 10(-3), where eta(EW) is the electroweak correction factor. Alternatively, assuming the model-independent form-factor parametrization of Boyd, Grinstein, and Lebed and using lattice QCD data from the FNAL/MILC and HPQCD collaborations, we find eta(EW)vertical bar V-cb vertical bar = (41.10 +/- 1.14) x 10(-3).