  We study the CP-violating asymmetry {\cal A}_{\rm CP}, which arises, in
\eta\to\pi^+\pi^- e^+e^-, from the angular correlation of the e^+ e^- and
\pi^+\pi^- planes due to the interference between the magnetic and electric
decay amplitudes. With the phenomenologically determined magnetic amplitude and
branching ratio as input, the asymmetry, induced by the electric bremsstrahlung
amplitude through the CP-violating decay \eta\to\pi^+\pi^-, and by an
unconventional tensor type operator, has been estimated respectively. The upper
bound of {\cal A}_{\rm CP} from the former is about 10^{-3}, and the asymmetry
from the latter might be up to O(10^{-2}). One can therefore expect that this
CP asymmetry would be an interesting CP-violating observable for the future
precise measurements in the \eta factories.
