  We study the production of hyperon resonances in the
$p\bar{p}\to\bar{\Lambda}\Sigma\eta$ reaction within an effective Lagrangian
approach. The model includes the production of $\Sigma(1750)$ and
$\Lambda(1670)$ in the intermediate state excited by the $K$ and $K^*$ meson
exchanges between the initial proton and antiproton. Due to the large coupling
of $\Sigma(1750)\Sigma\eta$ vertex, $\Sigma(1750)$ is found a significant
contribution near the threshold in this reaction. We provide total and
differential cross section predictions for the reation and discuss the possible
influence of $\Sigma(1750)\Sigma\eta$ vertex coupling and model parameters,
which will be useful in future experimental studies. This reaction can provide
a platform for studying the features of $\Sigma(1750)$ resonance, especially
the coupling to $\Sigma\eta$ channel.
