  In this article, we study the vertexes $\Xi_Q^*\Xi'_Q V$ and $\Sigma_Q^*
\Sigma_Q V$ with the light-cone QCD sum rules, then assume the vector meson
dominance of the intermediate $\phi(1020)$, $\rho(770)$ and $\omega(782)$, and
calculate the radiative decays $\Xi_Q^*\to \Xi'_Q \gamma$ and $\Sigma_Q^*\to
\Sigma_Q \gamma$.
