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As an important sequential work of the S-wave $B_c^{(*)}$ ($^1S_0(^3S_1)$)meson production at the large hadron electron collider (LHeC), we investigatethe production of the P-wave excited $B_c^{**}$ states ($^1P_1$ and $^3P_J$with $J=0,1,2$) via photoproduction mechanism within the framework ofnonrelativistic QCD at the LHeC. Generally, the $e^-+P \to \gamma+ g\rightarrow B_c^{**} +b+ \bar{c}$ process is considered as the main productionmechanism at an electron-proton collider due to the large luminosity of thegluon. However, according to our experience on the S-wave $B_c^{(*)}$ mesonproduction at the LHeC, the extrinsic production mechanism, i.e., $e^-+P\to\gamma+c \rightarrow B_c^{**} +b$ and $e^-+P \to\gamma+\bar{b} \rightarrowB_c^{**}+\bar{c}$, could also provide dominating contributions at low $p_T$region. A careful treatment between these channels is performed and the resultson total and differential cross sections, together with main uncertainties arediscussed. Taking the quark masses $m_b=4.90\pm0.40$ GeV and $m_c=1.50\pm0.20$GeV into account and summing up all the production channels, we expect toaccumulate $(2.48^{+3.55}_{-1.75}) \times 10^4$ $B_c^{**}({^{1}P_1})$,$(1.14^{+1.49}_{-0.82}) \times 10^4$ $B_c^{**}({^{3}P_0})$,$(2.38^{+3.39}_{-1.74}) \times 10^4$ $B_c^{**}({^{3}P_1})$ and$(5.59^{+7.84}_{-3.93}) \times 10^4$ $B_c^{**}({^{3}P_2})$ events at the$\sqrt{S}=1.30~\rm{TeV}$ LHeC in one operation year with luminosity ${\cal L}=10^{33}$ cm$^{-2}$s$^{-1}$. With such sizable events, it is worth studying theproperties of excited P-wave $B_c^{**}$ states at the LHeC.

P-wave excited $B_c^{**}$ meson photoproduction at the LHeC