  Motivated by the newly observed narrow structures $\Omega_b(6316)^-$,
$\Omega_b(6330)^-$, $\Omega_b(6340)^-$, and $\Omega_b(6350)^-$ in the $\Xi_b^0
K^-$ mass spectrum, we investigate the strong decays of the low-lying
$\Omega_b$ states within the $^3P_0$ model systematically. According to their
masses and decay widths, the observed $\Omega_b(6316)^-$, $\Omega_b(6330)^-$,
$\Omega_b(6340)^-$, and $\Omega_b(6350)^-$ resonances can be reasonably
assigned as the $\lambda-$mode $\Omega_b(1P)$ states with $J^P=1/2^-, 3/2^-,
3/2^-$, and $5/2^-$. Meanwhile, the remaining $P-$wave state with $J^P=1/2^-$
should have a rather broad width, which can hardly be observed by experiments.
For the $\Omega_b(2S)$ and $\Omega_b(1D)$ states, our predictions show that
these states have relatively narrow total widths and mainly decay into the
$\Xi_b \bar K$, $\Xi_b^\prime \bar K$ and $\Xi_b^{\prime*} \bar K$ final
states. These abundant theoretical predictions may be valuable for searching
more excited $\Omega_b$ states in future experiments.
