The article presents the application of a nonlinear autoregressive neural network to predict the HIV infection rate in Poland. The prediction was made using neural network models with three training functions: Levenberg-Marquardt, Bayesian Regularization, and BFGS Quasi-Newton. Real data was used to predict the HIV infection rate. Due to lower testability during the COVID-19 pandemic, these data indicated a lower infection rate during this period. This fact did not significantly affect the prediction using the NAR neural network. The prediction results obtained using the NAR neural network, linear regression and exponential smoothing methods were compared. The presented research is important due to the increasing number of HIV infections worldwide. The use of artificial neural networks to predict the infection rate can help locate places that require intensified preventive measures.