Abstract: Radar target echo is usually under very strong background of clutters. The detection of small moving targets has been a difficult problem. Based on matching pursuit sparse representation technology, a novel radar small moving target detection algorithm is proposed in this paper. Firstly, by using the correlation and sparsity characteristics of radar clutters, the proposed algorithm modeling clutters as linear combinations of a trained over-complete dictionary, successfully improves the accuracy of clutter modeling. Then upon employing this model in the clutter suppression, targets can be detected effectively from background clutters. Simulation results confirm that the performance of this method outperforms the classical target detection algorithms and this algorithm can improve the results of small moving target detection.