We present a measurement of the decay B- -> tau- nu_bar using a data sample containing 657 million BB_bar pairs collected at the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. A sample of BB_bar pairs are tagged by reconstructing one B meson decaying semileptonically. We detect the B- -> tau- nu_bar candidate in the recoil. We obtain a signal with a significance of 3.6 standard deviations including systematic uncertainties, and measure the branching fraction to be Br(B- -> tau- nu_bar) = [1.54+0.38-0.37(stat)+0.29-0.31(syst)]*10^-4. This result confirms the evidence for B- -> tau- nu_bar obtained in a previous Belle measurement that used a hadronic B tagging method.