Dust pollution is one of the major environmental crises in the arid regions of Iran and there is a need to predict dust pollution and identify its controlling factors to help reduce its adverse effects on the livelihood of residents of these areas. Although deep neural networks (DNN) are powerful tools in the modelling of environmental phenomena, they are recognized as being challenging to interpret due to their black-box nature. To address this issue and understand the importance of each environmental control on dust pollution, game theory (i.e., Shapley values) was used to better understand the performance and interpretability of DNN models. Here, monthly mean values of precipitation, air temperature, surface wind speed, potential evapotranspiration, normalized difference vegetation index, normalized difference salinity index, Palmer drought severity index, soil heat flux, and surface pressure were selected as explanatory variables. The dust storm index (DSI), an indicator of dust pollution, was the predicted response variable for the cold and warm months. The results showed that the accuracies of the DNN model in predicting cold months DSI (CMDSI) and warm months DSI (WMDSI) were higher compared to other traditional machine learning algorithms. DNN model increased the R2 by 13% and 15% for predicting CMDSI and WMDSI, respectively, compared to the Random Forest model, which was the second most effective approach. According to the Shapley values, the most important controls on the occurrence of dust storms during the cold months of the study period (2000–2018) were wind speed, soil heat flux, and precipitation. During the warm months, wind speed was the most important controlling factor and was followed by precipitation, soil heat flux, and potential evapotranspiration. Overall, the results demonstrate the effectiveness of the DNN model and game theory in identifying the factors affecting dust pollution, which may help mitigate its impacts on the residents of western Iran.