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The aim of the work is to study the effect of the number of nodes in the hidden layer, learning rate, and input level offset on the recognition rate, speed of network convergence (learning time), and network complexity of a neural network for speaker recognition. We investigated the number of hidden nodes that give both a high recognition rate and a relatively simple network. A high recognition rate (more than 97) was achieved when we used 30 nodes at the hidden layer. The results show that the recognition rate (number of correct answers) increases with an increasing of hidden nodes. However, it changes slightly after reaching a value of 97.6% for 30 hidden nodes where no significant increase occurred. Also we look to optimize other parameters to achieve both high recognition rate and fewer learning iterations.