A measurement of fiducial and differential cross-sections for W+W- production in proton-proton collisions at sqrt(s)=13 TeV with the ATLAS experiment at the Large Hadron Collider using an integrated luminosity of 36.1fb-1 is presented. Events with one electron and one muon are selected, corresponding to the decay of the diboson system as WW->e nu mu nu. To suppress top-quark background, events containing jets with a transverse momentum exceeding 35 GeV are not included in the measurement phase space. The fiducial cross-section, six differential distributions and the cross-section as a function of the jet-veto transverse momentum threshold are measured and compared with several theoretical predictions. Constraints on anomalous weak boson self-interactions are also presented in the framework of a dimension-six effective field theory.