  In this paper, a new type of hybrid state, which consists of two valence
quarks and two valence antiquarks together with a valence gluon, the gluonic
tetraquark states, are investigated. Twenty-four currents of the the gluonic
hidden-charm tetraquark states in $[\bar{3}_c]_{c
q}\otimes[8_c]_{G}\otimes[3_c]_{\bar{c} \bar{q^\prime}}$ configuration are
constructed, and their mass spectrum are evaluated in the framework of QCD sum
rules with quantum numbers of $J^P=0^{+}$, $0^{-}$, $1^{-}$, and $1^{+}$. The
nonperturbative contributions up to dimension 8 are taken into account. The
results indicate that there may be exist 14 gluonic hidden-charm tetraquark
states, and their corresponding hidden-bottom partners are also evaluated. The
possible production and decay modes of the gluonic tetraquark states are
analyzed, which are hopefully measurable in BESIII, BELLEII, PANDA, Super-B,
and LHCb experiments.
