  We report on the perturbative $O(\alpha_s)$ correction to the light-cone QCD
sum rule for the $B\to \pi$ transition form factor $f^+$. The correction to the
product $f_Bf^+$ in leading twist approximation is found to be about 30%, that
is similar in magnitude to the corresponding $O(\alpha_s)$ correction in the
two-point sum rule for $f_B$. The resulting cancellation of large QCD
corrections in $f^+$ eliminates one important uncertainty in the sum-rule
prediction for this form factor.
