Radial Basis Function Neural Networks (RBF NNs) are one of the most applicable NNs in the classification of real targets. Despite the use of recursive methods and gradient descent for training RBF NNs, classification improper accuracy, failing to local minimum and low-convergence speed are defects of this type of network. In order to overcome these defects, heuristic and meta-heuristic algorithms have been conventional to training RBF network in the recent years. This study uses Stochastic Fractal Search Algorithm (SFSA) for training RBF NNs. The particles in the new algorithm explore the search space more efficiently by using the diffusion property, which is observed regularly in arbitrary fractals. To assess the performance of the proposed classifier, this network will be evaluated with the two benchmark datasets and a high-dimensional practical dataset (i.e., sonar). Results indicate that new classifier classifies sonar dataset six percent better than the best algorithm and its convergence speed is better than the other algorithms. Also has better performance than classic benchmark algorithms about all datasets.