A search is presented for gluinos decaying via the supersymmetric partner of the top quark using events with two same-sign leptons, jets, and missing transverse momentum. The analysis is performed with 2.05 fb(-1) of integrated luminosity from pp collisions at sqrt[s]=7 TeV collected by the ATLAS detector at the LHC. No excess beyond the standard model expectation is observed, and exclusion limits are derived for simplified models where the gluino decays via the supersymmetric partner of the top quark and in the minimal supergravity and constrained minimal supersymmetric standard model framework. In those scenarios, gluino masses below 550 GeV are excluded at 95% C.L. within the parameter space considered, significantly extending the coverage with respect to existing limits. Depending on the model parameters, gluino masses up to 750 GeV can also be excluded at 95% C.L.