  Recently, some very tight constraints of annihilating dark matter have been
obtained from gamma-ray data of the Milky Way and Milky Way dwarf spheroidal
satellite galaxies. In this article, we report that there are two excellent
galaxy clusters (A2877 and Fornax) which can provide interesting constraints
for annihilating dark matter. The lower limits of the dark matter mass for the
thermal relic annihilation cross section are 25 GeV, 6 GeV, 130 GeV and 100 GeV
respectively for the $e^+e^-$, $\mu^+\mu^-$, $\tau^+\tau^-$ and $b\bar{b}$
channels. For some configuration of our working assumptions, our results
improve the Fermi-LAT upper limits of annihilation cross sections by a factor
of $1.3-1.8$ for wide ranges of dark matter mass for $e^+e^-$, $\mu^+\mu^-$ and
$b\bar{b}$ channels, and a factor of $1.2-1.8$ for $\tau^+\tau^-$ channel with
dark matter mass $\le 100$ GeV. These limits basically rule out most of the
existing popular dark matter interpretation of the GeV excess in the Milky Way.
