This paper proposes a new Local Kernel Feature Analysis (LKFA) method for object recognition. LKFA captures the nonlinear local relationship in an image via kernel functions. Different from traditional kernel methods for object recognition, the proposed method does not need to reserve the training samples. LKFA is designed to extract the eigenvalue features from the Hermite matrix of a local feature representation, which we have theoretically proven its robustness to noise and perturbations. Experiment results on palmprint and face recognitions demonstrated the effectiveness of the proposed LKFA that significantly improved the performance of the local feature based object recognition method.