The purpose of the paper is to demonstrate that the performance of an elite female swimmer in the finals of the 200-m backstroke at the Olympic Games 2000 in Sydney can be predicted by means of the nonlinear mathematical method of artificial neural networks (Multi-Layer Perceptrons). The data consisted of the performance output of 19 competitions (200-m backstroke) prior to the Olympics and the training input data of the last 4 weeks prior to each competition. Multi-Layer Perceptrons with 10 input neurons, 2 hidden neuron, and 1 output neuron were used. Since the data of 19 competitions are insufficient to train such networks, the training input and competition data of another athlete were used in the training processes of the neural networks to pre-train the neural networks. The neural models were validated by the "leave-one-out" method, then the neural models were used to predict the Olympic competitive performance. The results show that the modeling was very precise; the error of the prediction was only 0.05 s, with a total swim time of 2:12.64 min:s.