As an efficient sparse representation algorithm, orthogonal matching pursuit (OMP) has attracted massive attention in recent years. However, OMP and most of its variants estimate the sparse vector using the mean square error criterion, which depends on the Gaussianity assumption of the error distribution. A violation of this assumption, e.g., non-Gaussian noise, may lead to performance degradation. In this paper, a correntropy matching pursuit (CMP) method is proposed to alleviate this problem of OMP. Unlike many other matching pursuit methods, our method is independent of the error distribution. We show that CMP can adaptively assign small weights on severely corrupted entries of data and large weights on clean ones, thus reducing the effect of large noise. Our another contribution is to develop a robust sparse representation-based recognition method based on CMP. Experiments on synthetic and real data show the effectiveness of our method for both sparse approximation and pattern recognition, especially for noisy, corrupted, and incomplete data.