  Within the framework of NRQCD, we calculate the production of excited doubly
heavy baryons $\Xi_{bQ}$ through the semi-inclusive production process
$t\rightarrow \langle bQ\rangle[n]\rightarrow \Xi_{bQ}+ \bar {Q} + W^+ $, where
$Q= b$ or $c$ quark. The intermediate diquark state $\langle bQ\rangle[n]$ is
in the excited $P$-wave state, including $[^1P_1]$ and $[^3P_J]$ ($J=$0, 1 or
2) in both color antitriplet state $\mathbf{\mathbf{\overline 3}}$ and color
sixtuplet state $\mathbf{6}$, that is, $\langle
bc\rangle[^{1}P_{1}]_{\mathbf{\overline 3}/ \mathbf{6}}$, $\langle
bc\rangle[^{3}P_{J}]_{\mathbf{\overline 3}/ \mathbf{6}}$, $\langle
bb\rangle[^{1}P_{1}]_{\mathbf{\overline 3}}$, and $\langle
bb\rangle[^{3}P_{J}]_{\mathbf{6}}$. We find that the contributions from the
P-wave states are about one order lower than the S-wave contributions, and this
conclusion is consistent with others. We also analyze the invariant mass and
angle differential distributions, and the theoretical uncertainty from the mass
parameters and the renormalization scale. Finally, we can expect that about
$1.14 \times10^{3-5}$ events of excited $\Xi_{bc}$ and $2.47 \times10^{1-3}$
events of excited $\Xi_{bb}$ can be produced per year at the LHC or HL-LHC with
$\mathcal{L}$ =$10^{34-36}~\rm{cm}^{-2}~\rm{s}^{-1}$.
