Neural network-based methods such as deep neural networks show great efficiency for a wide range of applications. In this paper, a deep learning-based hybrid approach to forecast the yearly revenue passenger kilometers time series of Australia’s major domestic airlines is proposed. The essence of the approach is to use a resilient error backpropagation algorithm with dropout for “tuning” the polynomial neural network, obtained as a result of a multi-layered GMDH algorithm. The article compares the performance of the suggested algorithm on the time series with other popular forecasting methods: deep belief network, multi-layered GMDH algorithm, Box-Jenkins method and the ANFIS model. The minimum reached MAE of the proposed algorithm was approximately 25% lower than the minimum MAE of the next best method – GMDH, thus indicating that the practical application of the algorithm can give good results compared with other well-known methods.