  The $\Xi_b(6227)$ baryon with the quantum number $J^P=1/2^{-}$ is considered
as a molecular state composed of a $\Sigma_b$ baryon and $\bar{K}$ meson. The
partial decay widths of the $\Sigma_b\bar{K}$ molecular state into
$\Xi_b\gamma$ and $\Xi_b^{'}\gamma$ final states through hadronic loops are
evaluated with the help of the effective Lagrangians. The partial widths for
the $\Xi_b(6227)\to\gamma\Xi_b$ and $\Xi_b(6227)\to\gamma\Xi^{'}_b$ are
evaluated to be about 1.50-1.02 KeV and 17.56-24.91 KeV, respectively, which
may be accessible for the LHCb. Based on our results we argue that an
experimental determination of the radiative decay width of $\Xi_b(6227)$ is
important for the understanding of its intrinsic properties.
