This paper presents a new hybrid model that combines the seasonal trend model (STR) and the Elman neural network (ENN) to forecast seasonal time series with high accuracy and to provide accurate forecasts of seasonal time series. The model is based on dividing the time series into three components: trend, seasonality, and residual components. The STR model first divides the time series into these three components, and then the ENN is trained on each component separately to predict each part. The final results are then combined to obtain the overall forecast of the time series. The model was tested on monthly carbon dioxide emissions data from January 1995 to April 2020. The results showed that the hybrid model performed better than the individual models, achieving a mean absolute error (MAE) of 0.0099 and a mean square error (MSE) of \(3.42769 \times 10^{ - 4}\) . These results reflect the model’s ability to forecast seasonal time series with high accuracy, making it suitable for use in long-term forecasting applications.