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 sigma(fid.)(W +/- Z -> L'vll) = 63.2 +/- 3.2 (stat.) +/- 2.6 (sys.) +/- 1.5 (lumi.) fb. In comparison, the next-to-leading-order Standard Model prediction is 53.4(-2.8)(+3.6) fb. The extrapolation of the measurement from the fiducial to the total phase space yields sigma(tot.)(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(-1.0)(+1.1) 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.