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We present a determination of the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element |V cb | using the decay B → D ν ( = e, µ) based on 711 fb −1 of e + e − → Υ(4S) data recorded by the Belle detector and containing 772 × 10 6 BB 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 isospinaveraged branching fraction of the decay B → D ν is found to be B(B 0 → D − + ν ) = (2.31 ± 0.03(stat) ± 0.11(syst))%. Analyzing the differential decay rate as a function of the hadronic recoil with the parameterization of Caprini, Lellouch and Neubert and using the form-factor prediction G(1) = 1.0541 ± 0.0083 calculated by FNAL/MILC, we obtain ηEW|V cb | = (40.12 ± 1.34) × 10 −3 , where ηEW is the electroweak correction factor. Alternatively, assuming the model-independent form-factor parameterization of Boyd, Grinstein and Lebed and using lattice QCD data from the FNAL/MILC and HPQCD collaborations, we find ηEW|V cb | = (41.10 ± 1.14) × 10 −3 .