Recently, a lot of attention was paid to the improvement of methods which are used to air quality forecasting. Artificial neural networks can be applied to model these problems. Their advantage is that they can solve the problem in the conditions of incomplete information, without the knowledge of the analytical relationship between the input and output data. In this paper we applied artificial neural networks to predict the PM 10 concentrations as factors determining the occurrence of smog phenomena. To create these networks we used meteorological data and concentrations of PM 10. The data were recorded in 2014 and 2015 at three measuring stations operating in Krakow under the State Environmental Monitoring. The best results were obtained by three-layer perceptron with back-propagation algorithm. The neural networks received a good fit in all cases.