A measurement of the Standard Model Higgs boson produced in association with a W or Z boson and decaying into a pair of τ-leptons is presented. This search is based on proton-proton collision data collected at s=13 TeV by the ATLAS experiment at the LHC corresponding to an integrated luminosity of 140 fb−1. For the Higgs boson candidate, only final states with at least one τ-lepton decaying hadronically (τ→hadrons+ντ) are considered. For the vector bosons, only leptonic decay channels are considered: Z→ℓℓ and W→ℓνℓ, with ℓ=e,μ. An excess of events over the expected background is found with an observed (expected) significance of 4.2 (3.6) standard deviations, providing evidence of the Higgs boson produced in association with a vector boson and decaying into a pair of τ-leptons. The ratio of the measured cross-section to the Standard Model prediction is μVHττ=1.28−0.29+0.30(stat.)−0.21+0.25(syst.). This result represents the most accurate measurement of the VH(ττ) process achieved to date.