High-resolution optical remote sensing image registration is still a challenging task due to non-linearity in the intensity differences and geometric distortion. In this paper, an efficient method utilizing a hyper-graph matching algorithm is proposed, which can simultaneously use the high-order structure information and radiometric information, to obtain thousands of feature point pairs for accurate image registration. The method mainly consists of the following steps: firstly, initial matching by Uniform Robust Scale-Invariant Feature Transform (UR-SIFT) is carried out in the highest pyramid image level to derive the approximate geometric relationship between the images; secondly, two-stage point matching is performed to find the matches, that is, a rotation and scale invariant area-based matching method is used to derive matching candidates for each feature point and an efficient hyper-graph matching algorithm is applied to find the best match for each feature point; thirdly, a local quadratic polynomial constraint framework is used to eliminate match outliers; finally, the above process is iterated until finishing the matching in the original image. Then, the obtained correspondences are used to perform the image registration. The effectiveness of the proposed method is tested with six pairs of high-resolution optical images, covering different landscape types—such as mountain area, urban, suburb, and flat land—and registration accuracy of sub-pixel level is obtained. The experiments show that the proposed method outperforms the conventional matching algorithms such as SURF, AKAZE, ORB, BRISK, and FAST in terms of total number of correct matches and matching precision.