  In this talk, we briefly report the investigations of the mass spectra for
the $cc\bar c\bar c, bb\bar b\bar b$, $bc\bar b\bar c$ and $cc\bar b\bar b$
tetraquark states by using the QCD moment sum rule method. The calculations for
the fully-charm $cc\bar c\bar c$ tetraquarks have been successfully predicted
the existence of di-$J/\psi$ resonances including $X(6900)$ in LHCb's
observation. The quantum numbers for these resonance structures are also
suggested. More efforts are still needed in both theoretical and experimental
aspects to study the properties of these fully-heavy tetraquark states. They
may be observed at facilities such as LHCb, CMS and RHIC in the future.
