In recent years, although various research has been performed on object detection with clear weather images, little attention has been paid to object detection with foggy aerial images. In this paper, we address the problem of detecting objects in foggy aerial images. Firstly, we create the UIT-DroneFog dataset by implementing a fog simulator (taken from the imgaug library) on 15,370 aerial images collected from the UIT-Drone21 dataset. This dataset has its distinguishing characteristic of having dense motorbike density in Vietnam with 4 objects: Pedestrian, Motor, Car, and Bus. Secondly, we further leverage two state-of-the-art object methods: Guided Anchoring, and Double Heads. The experiment results show that Double Heads achieve a higher mAP score, with 33.20%. Additionally, we propose a method called CasDou, which is the combination of Cascade RCNN, Double Heads, and Focal Loss. CasDou remarkably improves the mAP score up to 34.70%. The comprehensive evaluation points out the advantages and limitations of each method, which is the fundamental basement for further work.