  In this article, we calculate the vector form factors $f^+_{K\pi}(Q^2)$ and
$f^-_{K\pi}(Q^2)$ within the framework of the light-cone QCD sum rules
approach. The numerical values of the $f^+_{K\pi}(Q^2)$ are compatible with the
existing theoretical calculations, the central value of the $f^+_{K\pi}(0)$,
$f^+_{K\pi}(0)=0.97$, is in excellent agreement with the values from the chiral
perturbation theory and lattice QCD. The values of the $|f^-_{K\pi}(0)|$ are
very large comparing with the theoretical calculations and experimental data,
and can not give any reliable predictions. At large momentum transfers with
$Q^2> 5GeV^2$, the form factors $f^+_{K\pi}(Q^2)$ and $|f^-_{K\pi}(Q^2)|$ can
either take up the asymptotic behavior of $\frac{1}{Q^2}$ or decrease more
quickly than $\frac{1}{Q^2}$, more experimental data are needed to select the
ideal sum rules.
