In this paper, we present a new face recognition approach based on dimensional surface matching. While most of existing methods use facial intensity images, a newest ones focus on introducing depth information to surmount some of classical face recognition problems such as pose, illumination, and facial expression variations. The presented matching algorithm is based first on ICP (Iterative Closest Point) that align rigidly facial surfaces and provides perfectly the posture of the presented probe model. Second, the similarity metric consists in computing geodesic maps on the overlapped parts of the aligned surfaces. The general paradigm consists in building a full 3D face gallery using a laser-based scanner (the on-line phase). At the on-line phase of identification or verification, a captured 2.5D face model (range image) is performed with the whole set of 3D faces from the gallery or compared to the 3D face model of the genuine, respectively. This probe model can be acquired from arbitrary viewpoint, with arbitrary facial expressions, and under arbitrary lighting conditions. Finally, We discuss some experimental results done on the ECL-IV2 new 3D face database.