  We propose a new estimate of the process $B \to (\rho, \omega)+ \gamma$ by
using the light-cone QCD sum rule. The aim is to choose the chiral quark
current operators in order to eliminate the uncertainty arising from the
chiral-even operators in the correlator. In the case of neglecting the
corrections from $\rho$-meson mass, the sum rules for form factors are
obtained, which are valid to the twist-three accuracy. The resulting branching
ratios are consistent with the experimental data.
