  In this paper, we study the single top and Higgs associated production $\rm
e^- p\rightarrow \nu_e \bar{t} \rightarrow \nu_e h \bar{q}(h\rightarrow
b\bar{b})$ in the top-Higgs FCNC couplings at the LHeC with the electron beam
energy of $E_{e}$ = 60 GeV and $E_{e}$ = 120 GeV, combination of a 7 TeV and 50
TeV proton beam. With the possibility of e-beam polarization ($p_{e}$ = 0,
$\pm0.6$), we distinct the Cut-based method and the Multivariate Analysis (MVA)
based method, and compare with the current experimental and theoretical limits.
It is shown that the branching ratio Br $\rm(t\to uh)$ can be probed to 0.113
(0.093) $\%$, 0.071 (0.057) $\%$, 0.030 (0.022) $\%$ and 0.024 (0.019) $\%$
with the Cut-based (MVA-based) analysis at ($E_{p}$, $E_{e}$) = (7 TeV, 60
GeV), ($E_{p}$, $E_{e}$) = (7 TeV, 120 GeV), ($E_{p}$, $E_{e}$) = (50 TeV, 60
GeV) and ($E_{p}$, $E_{e}$) = (50 TeV, 120 GeV) beam energy and 1$\sigma$
level. With the possibility of e-beam polarization, the expected limits can be
probed down to 0.090 (0.073) $\%$, 0.056 (0.045) $\%$, 0.024 (0.018) $\%$ and
0.019 (0.015) $\%$, respectively.
