Directly benefiting from the deep learning methods, object detection has witnessed a great performance boost in recent years. However, drone-view object detection remains challenging for two main reasons: (1) Objects of tiny-scale with more blurs w.r.t. ground-view objects offer less valuable information towards accurate and robust detection; (2) The unevenly distributed objects make the detection inefficient, especially for regions occupied by crowded objects. Confronting such challenges, we propose an end-to-end global-local self-adaptive network (GLSAN) in this paper. The key components in our GLSAN include a global-local detection network (GLDN), a simple yet efficient self-adaptive region selecting algorithm (SARSA), and a local super-resolution network (LSRN). We integrate a global-local fusion strategy into a progressive scale-varying network to perform more precise detection, where the local fine detector can adaptively refine the target's bounding boxes detected by the global coarse detector via cropping the original images for higher-resolution detection. The SARSA can dynamically crop the crowded regions in the input images, which is unsupervised and can be easily plugged into the networks. Additionally, we train the LSRN to enlarge the cropped images, providing more detailed information for finer-scale feature extraction, helping the detector distinguish foreground and background more easily. The SARSA and LSRN also contribute to data augmentation towards network training, which makes the detector more robust. Extensive experiments and comprehensive evaluations on the VisDrone2019-DET benchmark dataset and UAVDT dataset demonstrate the effectiveness and adaptivity of our method. Towards an industrial application, our network is also applied to a DroneBolts dataset with proven advantages. Our source codes have been available at https://github.com/dengsutao/glsan.