This Letter reports on a search for narrow high-mass resonances decaying into dilepton final states. The data were recorded by the ATLAS experiment in pp collisions at root s = 7 TeV at the Large Hadron Collider and correspond to a total integrated luminosity of 1.08 (1.21) fb(-1) in the e(+)e(-) (mu(+)mu(-)) channel. No statistically significant excess above the standard model expectation is observed and upper limits are set at the 95% C. L. on the cross section times branching fraction of Z' resonances and Randall-Sundrum gravitons decaying into dileptons as a function of the resonance mass. A lower mass limit of 1.83 TeV on the sequential standard model Z' boson is set. A Randall-Sundrum graviton with coupling k/(M) over bar Pl = 0.1 is excluded at 95% C. L. for masses below 1.63 TeV.