A measurement is presented of the ZZ production cross section in the ZZ -> 2l2l' decay mode with l = e, mu and l' = e, mu, tau in proton-proton collisions at root s = 7 TeV with the CMS experiment at the LHC. Results are based on data corresponding to an integrated luminosity of 5.0 fb(-1). The measured cross section sigma(pp -> ZZ) = 6.24(-080)(+0.86) (stat.)(-0.32)(+0.41) (syst.) +/- 0.14 (lumi.) pb is consistent with the standard model predictions. The following limits on ZZZ and ZZ-gamma anomalous trilinear gauge couplings are set at 95% confidence level: -0.011 < f(4)(Z) < 0.012, -0.012 < f(5)(Z) < 0.012, -0.013 < f(4)(gamma) < 0.015, and -0.014 < f(5)(gamma) < 0.014.