This thesis presents an analysis of the exclusive B → π + π − ν decay, where represents an electron or a muon. The analysis uses the complete Υ(4S) data sample collected by the Belle detector, corresponding to 711 fb −1. The events are selected by fully reconstructing one B meson into hadronic decay modes, consequently the properties of the other B meson, "the signal B", can be inferred via conservation laws. The branching ratio is extracted by using an extended binned maximum likelihood method and measured to be. This result is the first reported measurement of this decay. The dominant resonance in the dipion mass spectrum is the ρ 0 meson, observed with a branching ratio of B(B + → ρ 0 + ν ) = (1.71 ± 0.16 stat ± 0.10 syst ) × 10 −4. From this measurement, the magnitude of the CKM matrix element V ub is obtained as |V ub | = (3.56 ± 0.17 stat ± 0.10 syst, in agreement with the most precise measurement of this value from global fits to the B → π ν channel. Another resonance is reported with a product of branching ratios, B(B, with a 2.2σ statistical significance without taking into account systematic uncertainties.