Recently, it has been shown that the annihilation of 30–40 GeV dark matter particles through ƅƀ channel can satisfactorily explain the excess GeV gamma-ray spectrum near the Galactic Center. In this paper, we apply the above model to galaxy clusters and use the latest upper limits of gamma-ray flux derived from Fermi-LAT data to obtain an upper bound of the annihilation cross section of dark matter. By considering the extended density profiles and the cosmic ray profile models of 49 galaxy clusters, the upper bound of the annihilation cross section can be further tightened to <σν> ≤ 9 x 10⁻²⁶ cm³ s⁻¹. This result is consistent with the one obtained from the data near the Galactic Center. Copyright © 2016 Man Ho Chan.