A series of new physics scenarios predict the existence of the extra charged gauge boson W', which can induce the charged-current (CC) non-standard neutrino interactions (NSIs). The theoretical constraints on the simplified W' model and further on the CC NSI parameters $\widetilde{\epsilon}^{ qq'Y}_{\alpha\beta}$ from the partial wave unitarity and the W' decays are considered. The sensitivity of the process p p → W' → lν to the W' model at the LHC and high-luminosity (HL) LHC experiments is investigated by estimating the expected constraints on $\widetilde{\epsilon}^{qq'Y}_{\alpha\beta}$ (α = β = e or μ) using the Monte-Carlo (MC) simulation. We find that the interference effect plays an important role and the LHC can strongly constrain on $\widetilde{\epsilon}^{qq'L}_{\alpha\beta}$. Compared with the 13 TeV LHC with L = 139 fb-1, the expected constraints at the 14 TeV LHC with L = 3 ab-1 can be strengthened to about one order of magnitude. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.