To solve the problems of irregular hole shape and low accuracy of surface registration in an incomplete 3D model-repair process, a model-repair method was proposed to effectively maintain the natural hole boundary and restore the model surface details. First, we traced all points with unequal numbers of one-neighborhood edges and one-neighborhood triangles to detect the hole boundaries of the model. A method based on 2D mesh numbers was proposed to determine the matching candidate set for the incomplete model, and the optimal matching model was predicted based on the vertex-position error, edge-transition error, and orthogonal constraint, which were represented by double sparstiy. Then, the curvature was combined, cosine value of the boundary contour angle, and length of the line segments of the adjacent boundary points centered on the same boundary vertex to construct the feature descriptors that can effectively express the alignment relationship between the incomplete and fragmented models. Finally, the second-order umbrella operator was used to make the repair boundary of the model smooth. The experimental results demonstrate that the repair time is reduced by 19%—26% and the repair error is reduced by 35%, on average. This method avoids the limitations of large cracks and poorly realized surface details of the current model-restoration methods and can quickly and effectively repair the damaged model.