  Using data samples of $e^+e^-$ collisions collected with the BESIII detector
at eight center-of-mass energy points between 3.49 and 3.67 GeV, corresponding
to an integrated luminosity of 670 pb$^{-1}$, we present the upper limits of
Born cross sections and the effective form factor for the process
$e^+e^-\rightarrow\Omega^{-}\bar\Omega^{+}$. A fit to the cross sections using
a pQCD-derived energy dependent function shows no significant threshold effect.
The upper limit on the measured effective form factor is consistent with a
theoretical prediction within the uncertainty of 1$\sigma$. These results
provide new experimental information on the production mechanism of $\Omega$.
