3-D scanned face registration is the foundation and the prerequisite for 3-D faces statistical learning. To solve the problem of registering these digital points accurately, a 3-D faces registration method was developed using a non-rigid iterative closet point (ICP) algorithm combined with elastic deformation. By using the sparse 3-D feature vertices, the method fits high-resolution 3-D template meshes (3-D template faces) to 3-D face range scans (3-D target faces) through deformations step by step. This deformation process can be formulated as an optimization problem for the affine transformation at each vertex of the template face. In addition, this algorithm accelerates the registration process without sacrificing the registration accuracy by introducing elastic deformation. On this basis, a head missing data completion method for 3-D faces, combining the elastic deformation and the proposed 3-D registration, was developed to enhance the reality and the completeness of the 3-D face models. The experimental results show that this method is more robust than a widely used face completion method.