A study of W(+/-)Z production in proton-proton collisions at root s = 7 TeV is presented using data corresponding to an integrated luminosity of 4.6 fb(-1) collected with the ATLAS detector at the Large Hadron Collider in 2011. In total, 317 candidates, with a background expectation of 68 +/- 10 events, are observed in double-leptonic decay final states with electrons, muons and missing transverse momentum. The total cross-section is determined to be sigma(tot)(WZ) = 19.0(-1.3)(+1.4)(stat.) +/- 0.9(syst.) +/- 0.4(lumi.) pb, consistent with the Standard Model expectation of 17.6(-1.0)(+1.1) pb. Limits on anomalous triple gauge boson couplings are derived using the transverse momentum spectrum of Z bosons in the selected events. The cross-section is also presented as a function of Z boson transverse momentum and diboson invariant mass.