Vector-like quarks arise in many new theories beyond the Standard Model, which is driven by several theoretical issues. In a framework of the Standard Model simply extended by an SU(2) singlet vector-like bottom quark, we present a study of single production of such vector-like bottom quark at the LHeC. The work is preformed with assuming the LHeC with center of mass energy s=1.98 TeV and an integrated luminosity L=1000fb−1. We focus on the process e−p→νeB→νebH(orZ)→νebbb¯. The signal is searched in events with three b-jets within final state. Exclusion (discover) capability of the LHeC for the signal of the vector-like bottom quark are obtained at 2 σ (5 σ) confidence level. Our result demonstrates a significant improvement compared to previous relevant researches. We also discuss the capability of LHeC for the singlet B search with combined analysis from other experiments.