Sparse-representation is well-known for its promising performance in face recognition task. Recently, researchers have focused on optimizing the dictionary by learning the discriminative sparse model. On the other hand, symmetric positive definite (SPD) matrix descriptor has spurred great interest among computer vision community due to its inherent merits that enables features fusion. However SPD descriptors form a curved-geometry known as Tensor Manifold, which is incompatible to traditional vector-based dictionary learning methods. In order to close the gap between dictionary learning and SPD matrices, this paper proposes Tensor kernel supervised dictionary learning (TKSDL) for face recognition. TKSDL works in such a way by embedding the Tensor manifold into reproducing kernel Hilbert spaces by means of Tensor kernel functions. The discriminative dictionary is then learned by maximizing the Hilbert Schmidt independence criterion (HSIC) that leverages the class labels from the training data. Sparse coefficients are solved independently from the dictionary learning via a soft thresholding mechanism. Extensive experiments on the ORL, AR and FERET datasets are conducted to verify the efficiency of the proposed methods.