Conventional point cloud simplification algorithms have problems including nonuniform simplification, a deficient reflection of point cloud characteristics, unreasonable weight distribution, and high computational complexity. A simplification algorithm, namely, the multi-index weighting simplification algorithm (MIWSA), is proposed in this paper. First, the point cloud is organized with a bounding box and kd-trees to find the neighborhood of each point, and the points are divided into small segments. Second, the feature index of each point is calculated to indicate the characteristics of the points. Third, the analytic hierarchy process (AHP) and criteria importance through intercriteria correlation (CRITIC) are applied to weight these indexes to determine whether each point is a feature point. Fourth, non-feature points are judged as saved or abandoned according to their spatial relationship with the feature points. To verify the effect of the MIWSA, 3D model scanning datasets are calculated and analyzed, as well as field area scanning datasets. The accuracy for the 3D model scanning datasets is assessed by the surface area and patch numbers of the encapsulated surfaces, and that for field area scanning datasets is evaluated by the DEM error statistics. Compared with existing algorithms, the overall accuracy of the MIWSA is 5% to 15% better. Additionally, the running time is shorter than most. The experimental results illustrate that the MIWSA can simplify point clouds more precisely and uniformly.