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Considering the theoretical constraints on the charged-current (CC) non-standard neutrino interaction (NSI) parameters in a simplified W′ model, we study the sensitivities of the Large Hadron electron Collider (LHeC) and Future Circular Collider-hadron electron (FCC-he) to the CC NSI parameters through the subprocess e−q→W′→veq′. Our results show that the LHeC with L=100fb−1 is a little more sensitive to the CC NSI parameters than that of the high-luminosity (HL) LHC, and the absolute values of the lower limits on the CC NSI parameters at the FCC-he are smaller than those of the HL-LHC about two orders of magnitude.