A search for high-mass resonances decaying into tau(+)tau(-) final states using proton-proton collisions at root s = 8 TeV produced by the Large Hadron Collider is presented. The data were recorded with the ATLAS detector and correspond to an integrated luminosity of 19.5-20.3 fb(-1). No statistically significant excess above the Standard Model expectation is observed; 95% credibility upper limits are set on the cross section times branching fraction of Z' resonances decaying into tau(+)tau(-) pairs as a function of the resonance mass. As a result, Z' bosons of the Sequential Standard Model with masses less than 2.02 TeV are excluded at 95% credibility. The impact of the fermionic couplings on the Z' acceptance is investigated and limits are also placed on a Z' model that exhibits enhanced couplings to third-generation fermions.