Due to the rapid development of deep learning, the performance of object detection has greatly improved. However, object detection in high-resolution Unmanned Aerial Vehicles images remains a challenging problem for three main reasons: (1) the objects in aerial images have different scales and are usually small; (2) the images are high-resolution but state-of-the-art object detection networks are of a fixed size; (3) the objects are not evenly distributed in aerial images. To this end, we propose a two-stage Adaptive Region Selection Detection framework in this paper. An Overall Region Detection Network is first applied to coarsely localize the object. A fixed points density-based targets clustering algorithm and an adaptive selection algorithm are then designed to select object-dense sub-regions. The object-dense sub-regions are sent to a Key Regions Detection Network where results are fused with the results at the first stage. Extensive experiments and comprehensive evaluations on the VisDrone2021-DET benchmark datasets demonstrate the effectiveness and adaptiveness of the proposed framework. Experimental results show that the proposed framework outperforms, in terms of mean average precision (mAP), the existing baseline methods by 2.1% without additional time consumption.