Gabor-based region covariance matrix (GRCM) is a very flexible face descriptor where it allows different combination of features to be fused to construct a covariance matrix. GRCM resides on Tensor manifold where the computation of geodesic distance between two points requires the consideration of geometry characteristics of the manifold. Affine Invariant Riemannian Metric (AIRM) is the most widely used geodesic distance metric. However, it is computationally heavy. This paper investigates several geodesic distance metrics on Tensor manifold to find out the alternative speedy method for 2.5D face recognition using GRCM. Besides, we propose a feature-level fusion for 2.5D partial and 2D data to enhance the recognition performance.