Drones have been widely used for remote sensing applications. To perform high-quality drone image stitching, this paper first proposes a local and global structure-preserving alignment (LGSPA) method that aligns drone images from local dual feature-based and global pixel-based alignment perspectives, while maintaining local linear and global colinear image structures. To enable an optimal image stitching performance, we then propose a seam-adaptive weighting (SAW) scheme to enhance the local alignment accuracy under the guidance of a seam prior. On the ground of LGSPA and SAW, we further develop a seam-adaptive structure-preserving (SASP) image stitching framework to generate the final stitched drone images. Both qualitative and quantitative experimental results demonstrate that LGSPA and SASP are capable of generating higher-quality alignment and stitching results than several state-of-the-art methods over multiple challenging aerial scenarios, including low textures, repetitive textures, large parallax, wide baseline, and occlusions.