Results are presented from a search for a narrow, spin-2 resonance decaying into a pair of Z bosons, with one Z-boson decaying into leptons (e+e- or mu+mu-) and the other into jets. An example of such a resonance is the Kaluza--Klein graviton, G[KK], predicted in Randall--Sundrum models. The analysis is based on a 4.9 inverse femtobarn sample of proton-proton collisions at a center-of-mass energy of 7 TeV, collected with the CMS detector at the LHC. Kinematic and topological properties including decay angular distributions are used to discriminate between signal and background. No evidence for a resonance is observed, and upper limits on the production cross sections times branching fractions are set. In two models that predict Z-boson spin correlations in graviton decays, graviton masses are excluded lower than a value which varies between 610 and 945 GeV, depending on the model and the strength of the graviton couplings.