In this paper, we study the possibility of detecting the heavy vector-like top partner T in a simplified model with the decay channel T→tZ at the Large Hadron Electron Collider (LHeC). We first investigate the single top partner production process including the intergenerational mixing and the results show that the mixing between the top partner with the first generation can largely enhance the production cross section. We further study the observability of the single top partner through the process e+p→T(→tZ)ν¯e→t(→bjj′)Z(→ℓ+ℓ−)ν¯e at the LHeC with the proposed 140 GeV electron beam and 7 TeV proton beam. For some typical heavy T quark masses, the 3σ exclusion limits as well as the 5σ discovery region are respectively presented in terms of parameter space regions.