  We calculate the branching ratios of $B\to K_1\gamma$ at next-to-leading
order (NLO) of $\alpha_s$ where $K_1$ is the orbitally excited axial vector
meson. The NLO decay amplitude is divided into the vertex correction and the
hard spectator interaction part. The one is proportional to the weak form
factor of $B\to K_1$ transition while the other is a convolution between
light-cone distribution amplitudes and hard scattering kernel. Using the
light-cone sum rule results for the form factor, we have $\calB(B^0\to
K_1^0(1270)\gamma)=(0.828\pm0.335)\times 10^{-5}$ and $\calB(B^0\to
K_1^0(1400)\gamma)=(0.393\pm0.151)\times 10^{-5}$.
