The non-linear manifold structure property of inverse synthetic aperture radar (ISAR) images is analysed intensively, and it is pointed that the ISAR images can be viewed as a non-linear manifold of high-dimensional ISAR image space controlled by a few parameters, such as position, attitude and scale. The idea of non-linear manifold learning is introduced into ISAR target recognition, a new feature extraction and recognition method for 2-D ISAR images based on Locality Preserving Projections (LPP) algorithm and k-nearest neighbor classification is proposed. Firstly, the LPP algorithm is used to reduce the dimensionality of the ISAR images, and then four kinds of aircraft target are classified by k-nearest neighbor classification with rejection capability in the low-dimensional subspace. The simulated experiment results suggest that the LPP algorithm has the capability of finding the low-dimensional manifold structure embedded in the high-dimensional ISAR image space, and a higher recognition rate is acquired with the low-dimensional feature obtained by LPP.