  Stimulated by the newly discovered $\Omega(2012)$ resonance at Belle II, in
this work we have studied the OZI allowed strong decays of the low-lying $1P$-
and $1D$-wave $\Omega$ baryons within the $^3P_0$ model. It is found that
$\Omega(2012)$ is most likely to be a $1P$-wave $\Omega$ state with
$J^P=3/2^-$. We also find that the $\Omega(2250)$ state could be assigned as a
$1D$-wave state with $J^P=5/2^+$. The other missing $1P$- and $1D$-wave
$\Omega$ baryons may have large potentials to be observed in their main decay
channels.
