  In the past decade, gamma-ray observations and radio observations of our
Milky Way and the Milky Way dwarf spheroidal satellite galaxies put very strong
constraints on annihilation cross sections of dark matter. In this article, we
suggest a new target object (NGC 2976) that can be used for constraining
annihilating dark matter. The radio and x-ray data of NGC 2976 can put very
tight constraints on the leptophilic channels of dark matter annihilation. The
lower limits of dark matter mass annihilating via $e^+e^-$, $\mu^+\mu^-$ and
$\tau^+\tau^-$ channels are 200 GeV, 130 GeV and 110 GeV respectively with the
canonical thermal relic cross section. We suggest that this kind of large
nearby dwarf galaxies with relatively high magnetic field can be good
candidates for constraining annihilating dark matter in future analysis.
