Estimating transformations from degraded point sets is necessary for many computer vision and pattern recognition applications. In this paper, we propose a robust non-rigid point set registration method based on spatially constrained context-aware Gaussian fields. We first construct a context-aware representation (e.g., shape context) for assignment initialization. Then, we use a graph Laplacian regularized Gaussian fields to estimate the underlying transformation from the likely correspondences. On the one hand, the intrinsic manifold is considered and used to preserve the geometrical structure, and a priori knowledge of the point set is extracted. On the other hand, by using the deterministic annealing, the presented method is extended to a projected high-dimensional feature space, i.e., reproducing kernel Hilbert space through a kernel trick to solve the transformation, in which the local structure is propagated by the coarse-to-fine scaling strategy. In this way, the proposed method gradually recovers much more correct correspondences, and then estimates the transformation parameters accurately and robustly when facing degradations. Experimental results on 2D and 3D synthetic and real data (point sets) demonstrate that the proposed method reaches better performance than the state-of-the-art algorithms.