We report a measurement of the branching fraction of B+ -> tau(+) nu(tau) decays using a data sample of 772 x 10(6) B (B) over bar pairs, collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We reconstruct the accompanying B meson in a semileptonic decay and detect the recoiling B candidate in the decay channel B+ -> tau(+) nu(tau). We obtain a branching fraction of B(B+ -> tau(+) nu(tau)) = [1.25 +/- 0.28(stat.) +/- 0.27(syst.)] x 10-(4). This result is in good agreement with previous measurements and the expectation from the calculation based on the Standard Model.