Particle Swarm Optimization (PSO) algorithm has become more popular recently. It has been shown to be an effective optimization tool in most of the applications. In this paper, we have applied the PSO algorithm to a sample Artificial Neural Network (ANN) application, measured the improvement, and optimized the PSO parameters to improve results as much as possible. The application is character recognition of English numbers. Two indicators of accuracy of the results and processing time are taken in to account. The objective of this paper is to show that we can empirically adjust the PSO parameters to optimize PSO for the best results. Through several iterative processes of extracting improvements and adjusting the PSO parameters, we have recorded optimized PSO parameters and respective variances for similar applications. Indeed, the method can also be extended to alphabetic characters by just providing the input training patterns of each character. The details of the proposed approach and the simulation results are recorded in this paper.