  We present a measurement of the charmless semileptonic decay
$B^0\to\pi^-\ell^+\nu$ using a data sample containing 657$\times 10^6$
$B\bar{B}$ events collected with the Belle detector at the KEKB
asymmetric-energy $e^+e^-$ collider operating near the $\Upsilon(4S)$
resonance. We determine the total branching fraction of the decay,
$\mathcal{B}(B^0\to\pi^-\ell^+\nu)=(1.49\pm 0.04{(\mathrm{stat})}\pm
0.07{(\mathrm{syst})})\times 10^{-4}$. We also report a new precise measurement
of the differential decay rate, and extract the Cabibbo-Kobayashi-Maskawa
matrix element $|V_{ub}|$ using model-independent and -dependent approaches.
From a simultaneous fit to the measured differential decay rate and lattice QCD
results, we obtain $|V_{ub}|=(3.43\pm 0.33)\times 10^{-3}$, where the error
includes both statistical and systematic uncertainties.
