We investigate the stability of leptonic self-complementarity such that the sum of three mixing angles in the lepton sector is 90 degrees. Current experimental data of neutrino oscillation indicate that the self-complementarity can be satisfied within 3σ ranges of each mixing angle. Thus self-complementarity may be the key to study the flavor physics behind the standard model, and it is important to discuss its stability. We analyze renormalization group equations in the context of the minimal supersymmetric standard model for the self-complementarity. It is seen that one of the Majorana phases plays an important role for the stability of self-complementarity. We find some stable solutions against quantum corrections at low energy. An effective neutrino mass for the neutrinoless double-beta decay is also evaluated by the use of neutrino parameters giving rise to the stable solutions.