We present the first measurement of the Michel parameter ζ′ in the τ-→μ-ν¯μντ decay using the full data sample of 988 fb-1 collected by the Belle detector operating at the KEKB asymmetric energy e+e- collider. The method is based on the reconstruction of the μ-→e-ν¯eνμ decay-in-flight in the Belle central drift chamber and relies on the correlation between muon spin and its daughter electron momentum. We study the main sources of the background that can imitate the signal decay, such as kaon and pion decays-in-flight and charged particle scattering on the detector material. Highly efficient methods of their suppression are developed and applied to select 165 signal-candidate events. We obtain ζ′=0.22±0.94±0.42 where the first uncertainty is statistical, and the second one is systematic. The result is in agreement with the Standard Model prediction of ζ′=1.