  As one category of vector boson fusion, photo-production is one important
production mechanism at $e$-$p$ colliders. A future $e$-$p$ collider -- Large
Hadron-electron Collider (LHeC) has been discussed as a "Higgs factory"
candidate where the Higgs boson produced via weak boson fusion (WBF) at the
LHeC plays an important role in precision measurement of Yukawa couplings. On
the other hand, a measurement of photo-production of the Higgs boson, if
possible, might be complementary to the measurement of Higgs to di-photon
partial decay width $\Gamma({h\to\gamma\gamma})$. In this paper, we study the
possibility of measuring this production process at the LHeC with the help of
the photon PDFs published in recent years. This process has a clean final state
without additional colored particles in the detectable region other than the
decay products of the Higgs. We compute the cross sections of all related
processes and find that the production rate is at the same order as the neutral
current WBF production of Higgs boson with missing forward jets. However, a
detailed phenomenological study of various Higgs decay channels shows that even
in the most promising semi-leptonic $WW$ channel, the feasibility of
identifying such photo-production is negative due to an irreducible
photo-production of $W^{+}W^{-}$.
