We study the tetraquark states with I^G J^{PC}=1^- 1^{-+} in the QCD sum rule. After exhausting all possible flavor structures, we analyses both the SVZ and finite energy sum rules. Both approaches lead to a mass around 1.6 GeV for the state with the quark contents q q q_bar q_bar, and around 2.0 GeV for the state with the quark contents q s q_bar s_bar. The flavor structure 3_bar * 6_bar + 6 * 3 is preferred. Our analysis strongly indicates that both pi1(1600) and pi1(2015) are also compatible with the exotic tetraquark interpretation, which are sometimes labeled as candidates of the 1^{-+} hybrid mesons. Moreover one of their dominant decay modes is a pair of axial-vector and pseudoscalar mesons such as b1(1235) pi, which is sometimes considered as the characteristic decay mode of the hybrid mesons.