In order to preserve the local structure of the image space, locality preserving projection (LPP) is applied to palmprint recognition. In small-size-sample cases such as image recognition, the matrix of the eigenvalue equation is singular. The traditional solution is to utilize the principal component analysis (PCA) as a pre-processing step aiming to reduce the dimensionality of the palmprint space, then LPP is applied to extract feature. Since the projection criterion of the PCA and that of LPP are essentially different, the pre-processing step to reduce the dimensionality using the PCA could result in the loss of some important discriminatory information. To solve the above problem, the three-methods, the three-level wavelet transform, image down-sample, and the mean of block segmentation, are presented to reduce palmprint space dimensionality. Then LPP is used to extract the local features. The cosine distance between two feature vectors is calculated to match palmprint. The three algorithms are tested in PolyU plmprint database. The results show that the recognition performance of the algorithm exceeds PCA and PCA+LPP. The all time is less than 0.1 s including feature extraction and matching time, so it has the advantages of quickness, high efficiency, and easy realization.