2.5D face recognition, which leverages both texture and range facial images often outperform sole texture 2D face recognition as the former provides additional unique information than the latter. The 2.5D face recognition naturally incurs higher computational load since two types of data are involved. In this paper, we investigate the possibility of just using range facial image alone for recognition. Gabor-based region covariance matrix (GRCM) is a flexible face feature descriptor that is capable to capture the geometrical and statistical properties of a facial image by fusing the diverse facial features into a covariance matrix. Here, we attempt to extract several feature derivatives from the range facial image for GRCM. Since GRCM resides on the Tensor manifold, geodesic and reparameterized distances of Tensor manifold are used as dissimilarity measures of two GRCMs. Thus, the accuracy performance of range image derivatives with several distance metrics on Tensor manifold is explored. Experimental results show the effectiveness of the range image derivatives and the flexibility of the GRCM in 2.5D face recognition.