Flight delay prediction is a major topic in intelligent airport management systems, which emphasizes the use of historical data and potential features to estimate whether a future flight will delay. However, many factors affect flight delays, and these factors can be categorized into weather features (e.g., temperature, humidity, and wind speed) and non-weather features (day-of-month, day-of-week, scheduled departure and arrival time). Moreover, the impacts of weather and non-weather factors on flight delays are different. Weather features play a more important role in adverse weather conditions and are the main reason for long flight delays. When the weather condition changes from severe to non-severe, non-weather features are the main reason for flight delays, and the caused delays are relatively short. Such different impacts on flight delays raise a strong need for considering the priority information of weather and non-weather features in flight delay prediction. In this paper, we design a variant of the Random Forest model to consider the priority information of weather and non-weather features to predict flight delays. A clustering algorithm-based analysis approach is developed to assess the impact of weather and non-weather features on flight delays and draw conclusions on the priority information of weather and non-weather features. A probability sampling method is embedded in the Random Forest at the feature selection stage to perform a prior choice for weather and non-weather features to help select the key influential features. Experiments are carried out on U.S. domestic flights in July 2018, and the comparison results demonstrate that the proposed model can significantly increase flight delay prediction accuracy.