In this paper, a robust non-rigid feature matching approach for image registration with geometry constraints is proposed. The non-rigid feature matching approach is formulated as a maximum likelihood (ML) estimation problem. The feature points of one image are represented by Gaussian mixture model (GMM) centroids, and are fitted to the feature points of the other image by moving coherently to encode the global structure. To preserve the local geometry of these feature points, two local structure descriptors of the connectivity matrix and Laplacian coordinate are constructed. The expectation maximization (EM) algorithm is applied to solve this ML problem. Experimental results demonstrate that the proposed approach has better performance than current state-of-the-art methods.