  The new vector-like top partners with charge $2/3$ are a typical feature of
many new physics models beyond the Standard Model (SM). We propose a search
strategy for single production of top partners $T$ focusing on both the $T\to
Wb$ and $T\to th$ decay channels at the Large Hadron Electron Collider (LHeC).
Our analysis is based on a simplified model in which the top partner is an
$SU(2)$ singlet, with couplings only to the third generation of SM quarks. We
study the observability of the single $T$ through the processes $e^{+}p \to
T(\to bW^{+})\bar{\nu}_{e}\to b\ell^{+}+ \not E_T^{miss}$ and $e^{+}p \to T(\to
th)\bar{\nu}_{e}\to t(\to jj'b)h(\to b\bar{b}) \not E_T^{miss}$ at the LHeC
with the proposed 140 GeV electron beam (with $80\%$ polarization) and 7 TeV
proton beam. For three typical $T$-quark masses (800, 900 and 1000 GeV), the
$3\sigma$ exclusion limits on the $TWb$ coupling are respectively presented for
various values of the integrated luminosity.
