  Inspired by the newly observed $\Omega(2012)$ state at Belle II, we
investigate the two-body strong decays of $\Omega$ baryons up to $N=2$ shell
within the chiral quark model. Our results indicate that: (i) the newly
observed $\Omega(2012)$ state could be assigned to the spin-parity $J^P=3/2^-$
state $|70,^210,1,1,\frac{3}{2}^-\rangle$ and the experimental data can be
reasonably described. However, the spin-parity $J^P=1/2^-$ state
$|70,^210,1,1,\frac{1}{2}^-\rangle$ and spin-parity $J^P=3/2^+$ state
$|56,^410,2,0,\frac{3}{2}^+\rangle$ can't be completely excluded. (ii) The
$D$-wave states in the $N=2$ shell are most likely to be narrow states with a
width of dozens of MeV and have a good potential to be observed in the $\Xi K$
and/or $\Xi(1530)K$ channels in future experiments. The $\Omega(2250)$
resonance listed in PDG may be a good candidate of the $J^P=5/2^+$ $1D$ wave
state $|56,^410,2,2,5/2^+\rangle$.
