Since the premature convergence phenomenon of genetic algorithms (GAs) degrades the performances of GAs significantly, solving this problem provides a lot of effects to the performances of GAs. In this paper, we propose a selective mutation method in order to improve the performances of GAs by alleviating this phenomenon. In the selective mutation, individuals are additionally mutated at the specific region according to their ranks. From this selective mutation, individuals with low ranks are changed a lot and those with high ranks are changed small in the phenotype. Finally, some good individuals search around them in detail and the other individuals have more chances to search new areas. This results in enhancing the performances of GAs through alleviating of the premature convergence phenomenon. We measured the performances of our method with four typical function optimization problems. It was found from experiments that our proposed method considerably improved the performances of GAs.