We study the seesaw realization of a A4 model with two Higgs singlets. In this model, the mixing angle 13 and leptogenesis are zero if the components of right handed neutrino mass matrix resulting from the two Higgs singlets are exact degenerate. We then study the minimal breaking of the model by a tiny shift between aforementioned components. This minimal breaking results in deviations of lepton mixing angles from their tri-bimaximal mixing values in which the current experimental value of 13 can be achieved. Besides, the baryon asymmetry of the Universe is successfully generated through non-zero leptogenesis by the decay of right handed neutrinos.