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Many new physics scenarios predict the existence of the extra charged gauge boson W′, which can induce the charged-current (CC) non-standard neutrino interactions (NSI). We investigate the constraints on the CC NSI in model-independent fashion via considering the W′ contributions to the lepton flavor violating (LFV) decays ℓi→ℓjγ, the pure leptonic flavor conservation (FC) decays ℓi→ℓjνiνj¯, leptonic decays of charged pion meson, semileptonic τ decays, and superallowed β decays. We find that the constraints on the pure leptonic CC NSI are generally stronger than the ones for the CC NSI with first generation quarks. The most stringent constraints on the CC NSI arise from the LFV decay μ→eγ. The constraints on the CC NSI from direct searches at the LHC are also discussed.