  Recent indirect searches of dark matter using gamma-ray, radio, and
cosmic-ray data have provided some stringent constraints on annihilating dark
matter. In this article, we propose a new indirect method to constrain
annihilating dark matter. By using the data of the G2 cloud near the Galactic
supermassive black hole Sgr A*, we can get stringent constraints on the
parameter space of dark matter mass and the annihilation cross section,
especially for the non-leptophilic annihilation channels $b\bar{b}$ and
$W^{\pm}$. For the thermal annihilation cross section, the lower bounds of dark
matter mass can be constrained up to TeV order for the non-leptophilic channels
with the standard spike index $\gamma_{\rm sp}=7/3$.
