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We consider the generation of the new light gauge boson Zμτ predicted by the U(1)Lμ−Lτ model via Zh1 associated production followed by the SM-like Higgs boson h1 decaying into a Zμτ pair process at future high-energy e+e− colliders. Taking into account the experimental constraints on the free parameters of the U(1)Lμ−Lτ model and the beam polarizations P(e−,e+)=(−0.8,0.3), P(e−,e+)=(0.8,−0.3) and P(e−,e+)=(0,0), we calculate the cross sections of Zμτ production and further investigate the observability of Zμτ production through the leptonic channel Image 1 and hadronic channel Image 2 at e+e− colliders. We find that the signal significance above 5σ for Zμτ detection can be achieved via both these two processes with appropriate parameter values and high integrated luminosity, and that the hadronic channel can offer a more detectable signature compared with the leptonic channel.