Abstract: A measurement of the polarisation of Wbosons produced in top-quark decays is presented, using proton-proton collision data at a centre-of-mass energy of v s= 13TeV. The data were collected by the ATLAS detector at the Large Hadron Collider and correspond to an integrated luminosity of 139fb(-1). The measurement is performed selecting t tevents decaying into final states with two charged leptons (electrons or muons) and at least two b-tagged jets. The polarisation is extracted from the differential cross-section distribution of the cos theta* variable, where theta(*) is the angle between the momentum direction of the charged lepton from the Wboson decay and the reversed momentum direction of the b-quark from the top-quark decay, both calculated in the Wboson rest frame. Parton-level results, corrected for the detector acceptance and resolution, are presented for the cos theta* angle. The measured fractions of longitudinal, left- and right-handed polarisation states are found to be f(0) = 0.684 +/- 0.005 (stat.)+/- 0.014 (syst.), f(L)= 0.318 +/- 0.003 (stat.)+/- 0.008 (syst.) and f(R)=-0.002 +/- 0.002 (stat.)+/- 0.014 (syst.), in agreement with the Standard Model prediction.