  The properties of $\Sigma$-hyperons in pure $\Sigma$ matter are studied with
the finite-density quantum chromo-dynamics sum rule (QCDSR) approach. The
$\Sigma\Sigma$ nuclear potential $U_\Sigma$ is most likely strongly attractive,
it could be about -50 MeV or even more attractive at normal nuclear density. If
this prediction is the case, the interactions between $\Sigma$-hyperons should
play crucial roles in the strange nuclear matter, when there are multi-$\Sigma$
hyperons. The bound state of double-$\Sigma$ maybe exist.
