A method is proposed to analyze the stability of a fuzzy controller and the method is applied to a fuzzy controller developed in this work to automatically control the steam generator water level in the pressurized water reactor (PWR). The stability analysis method is devised from the relationships between the fuzzy controller and the conventional PI (Proportional and Integral) controller. The relationships are derived from the theoretical analysis and modeling of the widely used fuzzy controller having two inputs (Error, Rate) and one output with triangular type membership functions. In addition, an analyzable 9-Rule fuzzy controller is designed and computer-simulated for the automatic control of the steam generator water level in the PWR to employ the developed stability analysis method. This study shows that the stability analysis method based on the comparison of the equivalent PI gain ranges of the fuzzy controller with that of a linear PI controller provides very meaningful ideas for the design of stable fuzzy controller through the computer simulations. Therefore, the method suggested in this work can be used in a confirmatory process to check the stability of a fuzzy controller designed with two inputs (error, rate) and also the method would be used as an useful guidance to efficiently design and tune the fuzzy controller.