  We study the double-gluon hybrid states with the quark-gluon contents $\bar q
q gg$ ($q=u/d$) and $\bar s s gg$. We construct twelve double-gluon hybrid
currents with various quantum numbers, five of which are found to be zero due
to some internal symmetries between the two gluon fields. We use the rest seven
currents to perform QCD sum rule analyses. Especially, the masses of the
double-gluon hybrid states with the exotic quantum number $J^{PC} = 2^{+-}$ are
calculated to be $M_{|\bar q q gg;2^{+-}\rangle} = 2.26^{+0.20}_{-0.25}$ GeV
and $M_{|\bar s s gg;2^{+-}\rangle} = 2.38^{+0.19}_{-0.25}$ GeV. Their two- and
three-meson decay patterns are also investigated.
