Evolutionary algorithms, Genetic algorithms in particular, are known to be robust and have been increasing popularity in the field of numerical optimization. Neural networks and genetic algorithms demonstrate powerful problem solving ability. They are based on quite simple principles, but take advantage of their mathematical nature: non-linear iteration. Neural networks with back-propagation learning showed results by searching for various kinds of functions. However, the choice of the basic global performance index ( parameter weights) often already determines the success of the training process. The study presents a hybrid controller system; has been optimized by genetic algorithm optimization tool. GA based optimization scheme for simultaneous coordination of multiple power system damping controllers. Local measurements will be considered as input signals to the damping controller. The proposed algorithm will be applied to tuning controller of a single machine infinite bus power system . All simulations will be carried out using MATLAB based package for nonlinear simulations of power systems Controllers will be designed using MATLAB neural network functions and genetic algorithms optimization tool.