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A genetic algorithm (GA) was used in this article to obtain optimal parameters of the automatic voltage regulator (AVR) which will assure the wanted response of the synchronous generator in all its working points of the capability diagram. From the third order mathematical model of the synchronous generator, equations which describe how gain and time constant of voltage dynamics of the synchronous generator change considering the working point are derived. A higher degree of freedom of tuning of the wanted response was achieved by two parameters which are overshoot and settling time of a reference model which describes the wanted dynamics of the excitation system. For one point of the capability diagram, analytical expressions of the optimal parameters of AVR are given for achieving the wanted response, while the optimal parameters of AVR which will assure minimal variation of responses of all working point of the capability diagram from the wanted response are obtained by using GA algorithm. Proposed GA optimized AVR which is realized by proportional and integrator (PI) controller was tested in a simulation by using the seventh and third order mathematical model and parameters of the synchronous generator of hydroelectric plant Peruća in Croatia.