The decay $J/psi to omega p bar p$ is studied using a $5.8 times 10^7$ $J/psi$ event sample accumulated with the BES II detector at the Beijing electron-positron collider. The decay branching fraction is measured to be $B(J/psi to omega p bar p)=(9.8pm 0.3pm 1.4)times 10^{-4}$. No significant enhancement near the $pbar p$ mass threshold is observed, and an upper limit of $B(J/psi to omega X(1860))B(X(1860)to pbar p)$$ $$< 1.5 times 10^{-5}$ is determined at the 95% confidence level, where X(1860) designates the near-threshold enhancement seen in the $pbar p$ mass spectrum in $J/psi to gamma p bar p$ decays.
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