A triangle-mesh-surface-simplification algorithm based on a constrained energy function is proposed. In the algorithm, vertices are deleted iteratively according to the dimension-less energy function, which represents the cost of surface modification by vertex deletion and subsequent hole re-triangulation. The energy function is used both for selecting a vertex with the minimum energy for deletion and for constraining the target curvature of the surface to be simplified. During simplification, the target curvature of the surface to be simplified is modified gradually by increasing upper limit constraints. The experimental results show that the proposed algorithm has the advantage that a set of parameters can be applied to various-scale data composed of a variety of sizes and shapes with boundary edges.