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Abstract Motivated by the newly observed narrow structures $$\Omega _b(6316)^-$$ Ωb(6316)- , $$\Omega _b(6330)^-$$ Ωb(6330)- , $$\Omega _b(6340)^-$$ Ωb(6340)- , and $$\Omega _b(6350)^-$$ Ωb(6350)- in the $$\Xi _b^0 K^-$$ Ξb0K- mass spectrum, we investigate the strong decays of the low-lying $$\Omega _b$$ Ωb states within the $$^3P_0$$ 3P0 model systematically. According to their masses and decay widths, the observed $$\Omega _b(6316)^-$$ Ωb(6316)- , $$\Omega _b(6330)^-$$ Ωb(6330)- , $$\Omega _b(6340)^-$$ Ωb(6340)- , and $$\Omega _b(6350)^-$$ Ωb(6350)- resonances can be reasonably assigned as the $$\lambda -$$ λ- mode $$\Omega _b(1P)$$ Ωb(1P) states with $$J^P=1/2^-, 3/2^-, 3/2^-$$ JP=1/2-,3/2-,3/2- , and $$5/2^-$$ 5/2- . Meanwhile, the remaining $$P-$$ P- wave state with $$J^P=1/2^-$$ JP=1/2- should have a rather broad width, which can hardly be observed by experiments. For the $$\Omega _b(2S)$$ Ωb(2S) and $$\Omega _b(1D)$$ Ωb(1D) states, our predictions show that these states have relatively narrow total widths and mainly decay into the $$\Xi _b {\bar{K}}$$ ΞbK¯ , $$\Xi _b^\prime {\bar{K}}$$ Ξb′K¯ and $$\Xi _b^{\prime *} {\bar{K}}$$ Ξb′∗K¯ final states. These abundant theoretical predictions may be valuable for searching more excited $$\Omega _b$$ Ωb states in future experiments.