In order to ensure the stable operation of blast furnace production, it is necessary to keep abreast of the trends in the gas permeability index of the blast furnace. As one of the key parameters to be monitored in the process of blast furnace smelting, the gas permeability index directly reflects the performance of the blast furnace in the actual production of the furnace. Continuous monitoring of the permeability index is required in the actual production of the blast furnace in order to effectively guarantee the stable and smooth operation of the blast furnace. The aim of this study is to accurately predict the trend in the blast furnace gas permeability index by constructing an intelligent prediction model and utilizing a data-driven approach to monitor the gas permeability index and ensure the stable operation of the blast furnace. First, based on the actual production data of a #2 blast furnace of an iron and steel enterprise, an isolated forest algorithm is applied to detect and eliminate the outliers in the original data, and then a data driver set is constructed after normalization of the deviation. Second, by analyzing the coupling mechanism between the blast furnace permeability and gas flow, as well as Spearman correlation analysis and MIC maximum information coefficient (MIC) analysis, key parameters are screened out as feature variables from the data-driven set. Finally, a wavelet neural network algorithm is used to construct an intelligent prediction model of the blast furnace gas permeability index. Compared with a BP neural network (BP), a particle swarm-optimized BP neural network (PSO-BP), and XGBoost, the wavelet neural network shows obvious advantages when the error is controlled in the range of ±0.1, and the prediction accuracy can reach 95.71%. The model is applied to the actual production of a #2 blast furnace of an iron and steel enterprise, and the results show that the predicted value of the blast furnace permeability index is highly consistent with the actual value of real-time blast furnace production, which verifies its excellent characteristics.