  We present a lattice QCD calculation of $B\to \pi l \nu$ semileptonic decay
form factors in the small pion recoil momentum region. The calculation is
performed on a quenched $16^3 \times 48$ lattice at $\beta=5.9$ with the NRQCD
action including the full 1/M terms. The form factors $f_1(v\cdot k_{\pi})$ and
$f_2(v\cdot k_{\pi})$ defined in the heavy quark effective theory for which the
heavy quark scaling is manifest are adpoted, and we find that the 1/M
correction to the scaling is small for the $B$ meson. The dependence of form
factors on the light quark mass and on the recoil energy is found to be mild,
and we use a global fit of the form factors at various quark masses and recoil
energies to obtain model independent results for the physical differential
decay rate. We find that the $B^*$ pole contribution dominates the form factor
$f^+(q^2)$ for small pion recoil energy, and obtain the differential decay rate
integrated over the kinematic region $q^2 >$ 18 GeV$^2$ to be $|V_{ub}|^2
\times (1.18 \pm 0.37 \pm 0.08 \pm 0.31)$ psec$^{-1}$, where the first error is
statistical, the second is that from perturbative calculation, and the third is
the systematic error from finite lattice spacing and the chiral extrapolation.
We also discuss the systematic errors in the soft pion limit for
$f^0(q^2_{max})$ in the present simulation.
