  We perform the comprehensive analysis of the polarization effects on the
e^+e^- -> W^+W^- process in the presence of the extra neutral gauge boson at
the LC energies. Consideration of the polarizations of the produced W bosons
and the beam polarizations provides substantial enhancements of the sensitivity
to the Z-Z' mixing angles in various models and the asymmetry variables also
give the strict constraints on the mixing angles. We find that the \chi-model
and the left-right model get the strict constraint from \sigma_{LL}^{unpol}
while the \psi-model and the \eta-model from the beam polarization asymmetry.
