  We study the CP violating effects in the decay of $\eta\to\pi^+\pi^-\gamma$.
We show that to have CP violation in the decay, one has to consider both linear
and circular photon polarizations. In the standard model, the polarizations are
vanishingly small. However, model-independently, i.e. using only experimental
constraint imposed by the limit on $Br(\eta\to\pi^+\pi^-)$ it can be up to
$O(10%)$. We also explore various possible operators and we find that the
tensor type operator, possibly arising from a nonzero CP violating electric
dipole moment of the strange quark, can induce a sizable linear photon
polarization.
