  We present an improved calculation of the $B\to K$ transition form factor
with chiral current in the QCD light-cone sum rule (LCSR) approach. Under the
present approach, the most uncertain twist-3 contribution is eliminated. And
the contributions from the twist-2 and the twist-4 structures of the kaon wave
function are discussed, including the $SU_f(3)$-breaking effects. One-loop
radiative corrections to the kaonic twist-2 contribution together with the
leading-order twist-4 corrections are studied. The $SU_f(3)$ breaking effect is
obtained, $ \frac{F^{B\to K}_{+}(0)}{F^{B\to\pi}_{+}(0)}=1.16\pm 0.03$. By
combining the LCSR results with the newly obtained perturbative QCD results
that have been calculated up to ${\cal O}(1/m^2_b)$ in Ref.\cite{hwf0}, we
present a consistent analysis of the $B\to K$ transition form factor in the
large and intermediate energy regions.
