Abstarct: Function Approximation, is one of the topics that many science from applied mathematics to computer science, are interested in. always, there was different methods for Function Approximation and by passing the time, they became more optimized or new methods has been introduced. One of this methods that is used in Function Approximation, is artificial Neural Network. Training artificial Neural Network is truly a kind of Function Approximation, because in order to get to the proper output, the parameters and rules of neurons of different laxyers must be estimated. Training the artificial Neural Network, usually is done by back propagation method or gradient descent algorithm, but sometimes heuristic algorithms is used for training the Neural Networks, that could has improvements and faults either. According to the researches that has been done by scientists till now, using optimization algorithms as a tool to train the Neural Networks could save the training time and increase the convergence rate and so it result in less final error. From the time, that optimization algorithms has been introduced, there was try to make changes and improvements and do combinations on this algorithms in order to increase the efficiency, decrease the training time and computational price, sometimes this is done by hybridizing this algorithms with other optimization methods and algorithms. In this thesis, I proposed a hybrid method of Particle Swarm Optimization algorithm and Tabu Search algorithm, and I has used this proposed method to train the Radial basis function artificial Neural Networks in order to Function Approximation. actually by hybridizing this algorithms, I used the advantages of this algorithms, and decrease disadvantages to get in to the better and more accurate results. After that, once I used gradient descent algorithm to train the Neural Network and in another time, I used classic Particle Swarm Optimization to train the Neural Network. This is done to certificate the results of proposed algorithm and make comparison between the given results of this proposed algorithm and results of training the Neural Network by gradient descent algorithm and Particle Swarm Optimization algorithm. To do this, I’ve done selecting some of parameters of Particle Swarm Optimization algorithm by Tabu Search algorithm, and analysis the result of this method on training the RBF Neural Network, and compared the results by gradient descent method and classic PSO algorithm on training the RBF Neural Network for Function Approximation.