Linear subspace analysis methods have been successfully applied to extract features for face recognition. But they are inadequate to represent the complex and nonlinear variations of real face images, such as illumination, facial expression and pose variations, because of their linear properties. In this paper, a nonlinear subspace analysis method, Kernel-based Nonlinear Discriminant Analysis (KNDA), is presented for face recognition, which combines the nonlinear kernel trick with the linear subspace analysis method - Fisher Linear Discriminant Analysis (FLDA).First, the kernel trick is used to project the input data into an implicit feature space, then FLDA is performed in this feature space. Thus nonlinear discriminant features of the input data are yielded. In addition, in order to reduce the computational complexity, a geometry-based feature vectors selection scheme is adopted. Another similar nonlinear subspace analysis is Kernel-based Principal Component Analysis (KPCA), which combines the kernel trick with linear Principal Component Analysis (PCA). Experiments are performed with the polynomial kernel, and KNDA is compared with KPCA and FLDA. Extensive experimental results show that KNDA can give a higher recognition rate than KPCA and FLDA.