Abstract: This paper focuses on a progressive geometry simplification method for the mobile computing terminals. Mobile 3D graphics on mobile terminals is the significant ongoing research. By considering the limitations of the mobile terminals, such as small display panel, low processor performance, narrow wireless bandwidth, the investigation of the progressive display of mobile 3D graphics is highly necessary. An iterative simplification method based on the reverse Kobbelt subdivision scheme is proposed to give a solution to displaying 3D graphics on mobile computing terminals. The proposed simplification method progressively simplifies the quadrangle mesh models, by iteratively dividing a mesh model into odd vertexes and even vertexes, and saving the even vertexes as a sparse model. Furthermore, by iteratively using odd vertexes as details and adding them to the sparse model, a progressive display pattern is introduced to support progressive display of LOD (level of detail) models and lossless reconstruction of the original mesh models. The new simplification method is compact and fast, and it can implement progressive display of the mobile 3D graphics efficiently. The experimental results on PDA Mio 336 show that this research will have a wider prospect in the mobile 3D graphics field, such as real-time interaction on mobile computing terminals.