Artificial neural networks are decision-making mechanisms inspired by the human nervous system. Many areas are widely used such as medicine, economics, machine learning. These nets generate an output value by passing input values through the layers. The input values are firstly multiplied by some weight values and sent to activation functions, thus, training is realized. The purpose of this training is to ensure that appropriate weight values are found. Meta-heuristic methods are widely used to find these weight values. In this study, Chaotic Map Cricket Algorithm was used to find the weight values. The weights obtained during the algorithm's operation were sent to the network and the weight matrix providing the minimum error was obtained. Since it is the first study on artificial neural network training with the Cricket Algorithm, the performance of the algorithm has been tried to be shown on the appropriate data sets in comparison with the Particle Swarm Optimization.