Gabor-based region covariance matrix (GRCM) is an emerging face feature descriptor, which has been shown promising for face recognition. The GRCM lies on Tensor manifold is inherently non-Euclidean, hence a disconnect exists between GRCM descriptor and vector-based classifiers, such as collaborative representation-based classifier (CRC). CRC is a strong alternative to sparse representation-based classifier yet enjoys high efficiency. In this paper, we bridge GRCM and CRC with kernel learning method. We investigate several geodesic distances on Tensor manifold that satisfy the Mercer's condition for kernel CRC construction as well as for speedy computation. Apart from that, we also devise two strategies to jointly combine the regionalized GRCMs with Tensor kernel CRC. Extensive experiments on the ORL and FERET datasets are conducted to verify the efficacy of the proposed method.