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In this work, we study the $1^{--}$ double-gluon charmonium ($\bar{c}ggc$)and bottomonium ($\bar{b} gg b$) hybrids in terms of QCD sum rules. We findthat the mass of $\bar{c}ggc$ hybrid lies in $M_{H_{c}}$ = $5.33 \sim 5.90$GeV, while in the bottom sector the mass of $\bar{b}ggb$ hybrid may be situatedin $M_{H_b} = 11.20 \sim 11.68$ GeV. The contributions up to dimension eight atleading order of $\alpha_s$ (LO) in the operator product expansion are takeninto account in the calculation. The double-gluon charmonium hybrid mesonpredicted in this work can decay into a pair of charmed mesons or a pair ofcharmed mesons together with a light meson. Especially, we propose to searchfor $\bar{c}ggc$ hybrid with $I^G(J^{PC})= 0^-(1^{--})$ in their decay channels$D \bar{D}/D^* \bar{D}/D^{*} \bar{D}^{*}$ with P wave and $D^* \bar{D}^{*}\pi/D^* \bar{D}^*\eta/D \bar{D}\rho/D \bar{D}\omega$ with S wave, which may beaccessible in Belle II, PANDA, Super-B, GlueX, and LHCb experiments.

Mass Predictions of Vector ($1^{--}$) Double-gluon Heavy Quarkonium Hybrids from QCD Sum Rules