We report on a measurement of the tau lepton polarization and its forward-backward asymmetry at the Z0 resonance using the OPAL detector. This measurement is based on analyses of the$$\tau \to e\bar v_e v_\tau $$,$$\tau \to \mu \bar v_\mu v_\tau $$, τ→π(K)vτ and τ→ρvτ from a sample of 30663 e+e+→τ+τ- events collected during the years 1990 to 1992. Assuming that the tau lepton decays according to V-A theory, we measure the average τ polarization to be
=(−14.9±1.9±1.3)% and the τ polarization forward-backward asymmetry to be ApolFB=(−8.9±2.2±0.9)%, where the first error is statistical and the second systematic. These results are consistent with the hypothesis of lepton universality. When combined under the assumption of universality, our results can be interpreted as a measurement of sin2θefflept=0.2321±0.0023 within the context of the Standard Model.