Kernel Fisher discriminant analysis (KFDA) method is a more prominent method in pattern recognition to extract non-linear characteristics. Kernel Fisher discriminal analysis was introduced in the palmprint recognition to extract non-linear characteristics. Wavelet transform was used to reduce palmprint image dimension based on retaining the original image information and features. Kernel Fisher discriminant analysis was used to extract features and the null-space KFDA method(ZKFDA) was introduced to solve the problem of small samples. A classifier to palmprint match was used based on minimum distance. Experimental results show that KFDA performs better than two-dimensional FLD(2DFLD) when the principal component numbers are different. ZKFDA performs better than KFDA in the average recognition rate, and computation is significantly decreased. The recognition performance of radial basis function is the best in the selection of kernel functions.