This paper presents a spectral method to matching a pair of feature sets based on isometric projection of matrix. In the proposed method, a graph is constructed to model the structure relationships between features. Then the correspondence is found by minimizing the inner product between two isometric projections of the weighted adjacency matrix of graph. Finally, transformation between the two feature sets is estimated according to correct correspondences. The performance of the proposed approach is better than the state-of-the-art method in terms of correct ratio under position perturbation and computation time. Experiments on a number of simulated data, synthetic and real-world images show the validity of the proposed algorithm.