In this paper, we introduce a novel, automatic method for 3D face recognition. A new feature called a spherical vector norms map of a 3D face is created using the normal vector of each point. This feature contains more detailed information than the original depth image in regions such as the eyes and nose. For certain flat areas of 3D face, such as the forehead and cheeks, this map could increase the distinguishability of different points. In addition, this feature is robust to facial expression due to an adjustment that is made in the mouth region. Then, the facial representations, which are based on Histograms of Oriented Gradients, are extracted from the spherical vector norms map and the original depth image. A new partitioning strategy is proposed to produce the histogram of eight patches of a given image, in which all of the pixels are binned based on the magnitude and direction of their gradients. In this study, SVNs map and depth image are represented compactly with two histograms of oriented gradients; this approach is completed by Linear Discriminant Analysis and a Nearest Neighbor classifier.