  We calculate the next-to-leading order (NLO) $\alpha_s$-corrections to the
contributions of the condensates $<\alpha G^2>$ and $<\bar qq>^2$ in the
current-current correlator of the hybrid current
$g\barq(x)\gamma_{\nu}iF_{\mu\nu}^aT^aq(x)$ using the external field method in
Feynman gauge. After incorporating these NLO contributions into the Laplace
sum-rules, the mass of the $J^{PC}$=$1^{-+}$ light hybrid meson is recalculated
using the QCD sum rule approach. We find that the sum rules exhibit enhanced
stability when the NLO $\alpha_s$-corrections are included in the sum rule
analysis, resulting in a $1^{-+}$ light hybrid meson mass of approximately 1.6
GeV.
