In this work, we present a new 3D face recognition method based on Speeded-Up Local Descriptor (SULD) of significant points extracted from the range images of faces. The proposed model consists of a method for extracting distinctive invariant features from range images of faces that can be used to perform reliable matching between different poses of range images of faces. For a given 3D face scan, range images are computed and the potential interest points are identified by searching at all scales. Based on the stability of the interest point, significant points are extracted. For each significant point we compute the SULD descriptor which consists of vector made of values from the convolved Haar wavelet responses located on concentric circles centred on the significant point, and where the amount of Gaussian smoothing is proportional to the radii of the circles. Experimental results show that the newly proposed method provides higher recognition rate compared to other existing contemporary models developed for 3D face recognition.