  In this work, we investigate the spectra of the prospective tetracharm and
tetrabottom baryonium, viz. the baryon-antibaryon states, in the framework of
QCD sum rules. The non-perturbative contributions up to dimension 10 are taken
into account. Numerical results indicate that there might exist 4 possible
tetracharm baryonium states with masses $(7.33\pm0.12)$, $(7.42\pm0.13)$,
$(7.68\pm0.17)$, and $(7.76\pm0.12)$ GeV for the quantum numbers of $0^{-+}$,
$1^{--}$, $0^{++}$, and $1^{++}$, respectively. The corresponding tetrabottom
partners are found lying respectively at $(19.41\pm 0.15)$, $(19.48\pm 0.15)$,
$(19.77\pm 0.19)$ and $(19.84\pm 0.19)$ GeV. Additionally, we also analyze the
spectra of the $\bar{\Xi}_{bc}\Xi_{bc}$ and $\bar{\Xi}_{cc}\Xi_{bb}$ baryonium
states, which lie in the range of $13.77-14.40$ GeV and $13.39-14.14$ GeV,
respectively. The possible baryonium decay modes are analyzed, which are
hopefully measurable in LHC experiments.
