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This paper presents a 3D face recognition algorithm using fast landmark detection and non-rigid iterative closest point (ICP) algorithm. The proposed approach can estimate the facial feature region using the anthropometric face model after pose correction, and accurately detect 9 facial landmarks (nose tip, sellion, inner and outer eye corners, nostrils and mouth center). An extension of ICP algorithm has also been proposed to matching the non-rigid 3D face shapes. Experimental results demonstrate that compared to the existing methods, the proposed approach can efficiently detect human facial landmarks and satisfactorily deal with the 3D face matching problem.