A search for high-mass resonances decaying into τ+τ− is performed using a data sample of pp collisions at s=7TeV. The data were collected with the CMS detector at the LHC and correspond to an integrated luminosity of 4.9 fb−1. The number of observed events is in agreement with the standard model prediction. An upper limit on the product of the resonance cross section and branching fraction into τ-lepton pairs is calculated as a function of the resonance mass. Using the sequential standard model resonance ZSSM′ and the superstring-inspired E6 model with resonance Zψ′ as benchmarks, resonances with standard model couplings with masses below 1.4 and 1.1 TeV, respectively, are excluded at 95% confidence level.