This paper proposes a rank-based control method of mutation probability for improving the performances of genetic algorithms (GAs). In order to improve the performances of GAs, GAs should not fall into premature convergence phenomena and should also be able to easily get out of the phenomena when GAs fall into the phenomena without destroying good individuals. For this, it is important to keep diversity of individuals and to keep good individuals. If a method for keeping diversity, however, is not elaborately devised, then good individuals are also destroyed. We should devise a method that keeps diversity of individuals and also keeps good individuals at the same time. To achieve these two objectives, we introduce a rank-based control method of mutation probability in this paper. We set high mutation probabilities to lowly ranked individuals not to fall into premature convergence phenomena by keeping diversity and low mutation probabilities to highly ranked individuals not to destroy good individuals. We experimented our method with typical four function optimization problems in order to measure the performances of our method. It was found from extensive experiments that the proposed rank-based control method could accelerate the GAs considerably.