  We calculate the masses of the $1^{-+}$ four quark states which decay
dominantly into $\rho\pi$ and $\eta\pi$ respectively by QCD sum rules approach.
We include the zero mode contribution and find it plays an important role in
the sum rules. We predict that the masses of the states $\eta\pi$ and $\rho\pi$
both are 1.4-1.5 GeV. This is close to the experimental candidates
$\pi_1(1370)$ and $\pi_1(1440)$.
