The production of W ± Z events in proton–proton collisions at a centre-of-mass energy of 13 TeV is measured with the ATLAS detector at the LHC. The collected data correspond to an integrated luminosity of 3.2 fb−1. The W ± Z candidates are reconstructed using leptonic decays of the gauge bosons into electrons or muons. The measured inclusive cross section in the detector fiducial region for leptonic decay modes is σ fid. W ± Z→ ν = 63.2 ± 3.2 (stat.) ± 2.6 (sys.) ± 1.5 (lumi.) fb. In comparison, the next-toleading-order Standard Model prediction is 53.4+3.6 −2.8 fb. The extrapolation of the measurement from the fiducial to the total phase space yields σtot. W ± Z = 50.6 ± 2.6 (stat.) ± 2.0 (sys.) ± 0.9 (th.) ± 1.2 (lumi.) pb, in agreement with a recent next-to-next-to-leading-order calculation of 48.2+1.1 −1.0 pb. The cross section as a function of jet multiplicity is also measured, together with the charge-dependent W+ Z and W − Z cross sections and their ratio.