This letter proposes a robust feature matching algorithm for remote sensing images based on l_q -estimator. We start with a set of initial matches provided by a feature matching method such as scale-invariant feature transform and then focus on global transformation estimation from contaminated observations and outliers elimination as well. We use an affine model to describe the global transformation and minimize a new cost function based on l_q -norm. We apply an augmented Lagrangian function and an alternating direction method of multipliers to solve such a nonconvex and nonsmooth optimization problem. Extensive experiments on real remote sensing data demonstrate that the proposed method is effective, efficient, and robust. Our method outperforms state-of-the-art methods and can easily handle situations with up to 90% outliers. In addition, the proposed method is much faster than RANSAC.