As the defocus status in non-contact signal acquisition for palmprint recognition might blur palmprint and degrade the performance of a recognition system, a novel scheme based on stable features was proposed for the blurred palmprint recognition. Firstly, a mathematical model of defocus degeneration was established. Then, the blur mechanism was analyzed in detail and the Laplacian Smoothing Transform (LST) was employed to extract low-frequency coefficients from blurred palmprint as stable features. Furthermore,the Euclidean distance between the feature vectors was used for matching and discriminating. With the experiments, the operation steps of the algorithm were given and the number of low-frequency coefficients were determined. The experiments based on the self-made SUT-D blurred palmprint database were performed. Obtained results show that the proposed algorithm can get Equal Error Rate (EER) of 17.101 7%, which has been maximally reduced by 7.908 4% compared with those from other typical recognition methods, such as traditional Discrete Cosine Transform (DCT), Eigen Palm and the Palm Code. These results show that the proposed scheme not only has higher recognition efficiency but also has a low dimension, so it significantly improves the performance of the blurred palmprint recognition systems.