  We study the $\rho\pi$ and $b_1\pi$ decay modes of the $1^{-+}$ light hybrid
state within the framework of light-cone QCD sum rules. We use both the tensor
current $\bar\psi\sigma_{\mu\nu}\psi$ and the derivative current
$\bar{\psi}\overleftrightarrow{D}_\mu\gamma_5\psi$ as interpolating currents to
calculate the partial decay width of the $b_1\pi$ decay mode. Comparing the sum
rules obtained by using different currents, we obtain $\Gamma(\pi_1\to b_1\pi)$
= 8--23, 32--86 and 52--151\,MeV for $m_{1^{-+}}$ = 1.6, 1.8 and 2.0\,GeV
respectively, which favour the results from the flux tube models and lattice
simulations. We also use the tensor current to study the $\rho\pi$ decay mode,
and although an extended stability criterion is needed, our results suggest a
small partial decay width.
