  In this paper, we investigate the nucleon-antinucleon static energies in the
Skyrme model with the product {\it Anzatz}. The calculation shows that in the
ungroomed $S\bar S$ (skyrmion and antiskyrmion) channel, which leads to rapid
annihilation, there exists a quasi-stable bound state which may give a natural
explanation for the near-threshold enhancement in the proton-antiproton
$(p\bar{p})$ mass spectrum reported by the BES Collaboration and the Belle
Collaboration. Similar to the phenomenological well potential of the deuteron,
we construct a phenomenological skyrmion-type potential to study this narrow
$p\bar{p}$-resonance in $ J/\psi\to \gamma p\bar{p}$. By this potential model,
a $p\bar{p}$ baryonium with small binding energies is suggested and the decay
width of this state is calculated by WKB approximation. In this picture the
decay is attributed to quantum tunnelling and $p\bar{p}$ annihilation.
Prediction on the decay mode from the baryonium annihilation at rest is also
pointed out.
