Ionic conductivity is a crucial parameter in the electrochemical applications of ionic liquids (ILs). Conventional methods to obtain this parameter, i.e., experimental measurements or theoretical calculations, are time-consuming and resourceintensive. Herein, we provide a machine learning (ML) method to predict the ionic conductivity for various ILs, where the dataset is composed of 5,700 data points for 414 ILs. Especially, all features of each IL are automatically extracted from the cations and anions by a graph neural network (GNN), which differs from the artificial feature selection in the previous work. Then we employ extreme gradient boosting (XGBoost), random forest (RF), decision tree (DT), and gradient boost regression tree (GBRT) to construct the ML models for predicting the ionic conductivity, demonstrating that all ML models utilizing the same GNN-based features accurately predict the ionic conductivity. Furthermore, we use the GNN+XGBoost model to perform a large-scale screening for 15,300 ILs created by pairing 180 cations with 85 anions under five different temperatures ranging from 275 to 325 K. Then we highlight 10 cations and 10 anions found in the top 5% ILs with high ionic conductivity from our predicted heat maps under all temperatures. Additionally, we compare the experimental and predicted temperature dependence of the ionic conductivity for five typical ILs, indicating the outstanding thermodynamic transferability of our GNN+ML models. Therefore, our GNN+ML framework proposed in this study presents a powerful tool for efficiently screening a wide range of IL properties, which offers experimental scientists a comprehensive road map to directionally design and synthesize high-performance ILs.