  The decay $J/\psi \rightarrow \omega p \bar{p}$ has been studied, using
$225.3\times 10^{6}$ $J/\psi$ events accumulated at BESIII. No significant
enhancement near the $p\bar{p}$ invariant-mass threshold (denoted as
$X(p\bar{p})$) is observed. The upper limit of the branching fraction
$\mathcal{B}(J/\psi \rightarrow \omega X(p\bar{p}) \rightarrow \omega p
\bar{p})$ is determined to be $3.9\times10^{-6}$ at the 95% confidence level.
The branching fraction of $J/\psi \rightarrow \omega p \bar{p}$ is measured to
be $\mathcal{B}(J/\psi \rightarrow \omega p \bar{p}) =(9.0 \pm 0.2\
(\text{stat.})\pm 0.9\ (\text{syst.})) \times 10^{-4}$.
