Inflation forecasting is one of the most important issues for the economies of countries, As the existing literature suggests, hybrid models will bring better prediction accuracy due to attention to both linear and non-linear dimensions. Furthermore, the use of ARDL model can include lags of other variables in tandem with having linear features. It should also be noted that LSTM models have a forgetting gate due to their non-linear estimation characteristics, and they can incorporate data with very distant lags in the model. Therefore, the combination of these two models can significantly improve the prediction accuracy. Accordingly, attempts have been made in the current study to compare ARDL, NARX, LSTM and ARDL-D-LSTM models with one another and to introduce a suitable model for predicting Iran's monthly inflation rate in the short-term and long-term time horizon. After estimating the monthly inflation rate of Iran in the period of 4/21/2005 to 8/22/2018 and testing the model on the data for the period of 9/22/2018 to 12/21/ 2020 it was found that the NARX model and the ARDL-D-LSTM hybrid model performed well respectively for short-term time horizon and the long-term horizon according to the RMSE criteria.