According to a type of normal nonlinear system, an indirect adaptive fuzzy (IAF) controller has been applied to those systems where no accurate mathematical models of the systems under control are available. To satisfy with system performance, an indirect accelerated adaptive fuzzy (IAAF) controller is proposed, and its general form is presented. The general form IAAF controller ensures necessary control criteria and system’s global stability using Lyapunov Theorem. It has been proved that the close-loop system error converges to a small neighborhood of equilibrium point. The optimal IAAF controller is derived to guarantee the process’s shortest settling time. Simulation results indicate the IAAF controller make the system more stable, accurate, and fast.