  In the past decade, gamma-ray observations and radio observations put strong
constraints on the parameters of dark matter annihilation. In this article, we
suggest another robust way to constrain the parameters of dark matter
annihilation. We expect that the electrons and positrons produced from dark
matter annihilation would scatter with the cosmic microwave background photons
and boost the photon energy to $\sim$ keV order. Based on the x-ray data from
the Draco dwarf galaxy, the new constraints for some of the annihilation
channels are generally tighter than the constraints obtained from 6 years of
Fermi Large Area Telescope (Fermi-LAT) gamma-ray observations of the Milky Way
dwarf spheroidal satellite galaxies. The lower limits of dark matter mass
annihilating via $e^+e^-$, $\mu^+\mu^-$, $\tau^+\tau^-$, $gg$, $u\bar{u}$ and
$b\bar{b}$ channels are 40 GeV, 28 GeV, 30 GeV, 57 GeV, 58 GeV and 66 GeV
respectively with the canonical thermal relic cross section. This method is
particularly useful to constrain dark matter annihilating via $e^+e^-$,
$\mu^+\mu^-$, $gg$, $u\bar{u}$ and $b\bar{b}$ channels.
