In this paper we propose a new method for 3D facial expression recognition. We make use of the Zernike moments, which are calculated in the depth image of a 3D facial point cloud. Combining, the Zernike moments along with the 3D point clouds and the depth images, we succeed in tackling problems arising in facial expression recognition due to affine transformations of the data, such as translation, rotation and scaling which, in other approaches are considered very harmful in the overall accuracy of a facial expression recognition algorithm. Support vector machines are used in order to classify the previously extracted features. Results are drawn in two publicly available databases for 3D facial expression recognition.