Our study focuses on the $\Lambda$-type P-wave bottom baryon states with the spin-parity $J^P=\frac{1}{2}^-$, $\frac{3}{2}^-$. We introduce an explicit P-wave between the two light quarks in the interpolating currents (and the two light quarks are antisymmetric in flavor space, therefore leads to the name $\Lambda$-type baryon) to investigate the $\Lambda_b$ and $\Xi_b$ states within the framework of the full QCD sum rules. The predicted masses show that the $\Xi_b(6087)$ and $\Xi_b(6095/6100)$ could to be the P-wave bottom-strange baryon states with the spin-parity $J^P=\frac{1}{2}^-$ and $\frac{3}{2}^-$, respectively, meanwhile, the $\Lambda_b(5912)$ and $\Lambda_b(5920)$ could be the P-wave bottom baryon states with the spin-parity $J^P=\frac{1}{2}^-$ and $\frac{3}{2}^-$, respectively. The $\Lambda_b(5920)$ and $\Xi_b(6095/6100)$ maybe have two remarkable under-structures or Fock components at least. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.