This paper proposes a self-organizing genetic algorithm (SOGA) with good global search properties and a high convergence speed. First, we introduce a new dominant selection operator that enhances the action of the dominant individuals, along with a cyclical mutation operator that periodically varies the mutation probability in accordance with evolution generation found in biological evolutionary processes. Next, the SOGA is constructed using the two operators mentioned above. The results of a nonlinear regression analysis demonstrate that the self-organizing genetic algorithm is able to avoid premature convergence with a higher convergence speed, and also indicate that it possesses self-organization properties. Finally, the new algorithm is used to optimize Proportional Integral Derivative (PID) controller parameters. Our simulation results indicate that a suitable set of PID parameters can be calculated by the proposed SOGA.