Sapphire single crystal another name white stone, which has wonderful thermal character, electrical properties, dielectric property, agreeability, Moth hardness is 9 level, good stability in high temperature, melting point 2030℃, has been widely used in the filed of industry, national defense, scientific research etc. And sapphire single crystal used as the substrate in the filed of various thin films. The sapphire single crystal substrate is demanded extreme low surface roughness. Up to mow, there are few papers dealing with the ultra-precision technology of sapphire single crystal substrate, especially the ultra-precision machining theory and the pivotal technology by which the final surface quality substrate is achieved. In this thesis, a systematic experimental study is presented on the chemical mechanical lapping process and fixed soft abrader grinding-polishing mechanism for sapphire single crystal substrate. The main studied contents and conclusions are as follows: On the basis of the physical and chemical properties of the sapphire single crystal, the chemical mechanical lapping is presented. The chemical mechanical lapping process of sapphire single crystal is investigated by using corundum abrasive with the size of 2.5\10um. The effects of lapping pressure, lapping plate rotational speed etc on surface roughness and material removal rate (MRR) are analyzed. The results show that there are the suitable lapping process parameters by which the low surface roughness and the high MAR can be achieved concurrently. The transient temperature and temperature transfer is calculated when the fixed soft abraders grinding-polishing experiment happening, on the basis of the stress analyzing when the sapphire single crystal fixed soft abraders grinding-polishing is occurring . Analyzing and simulating the moving trace of the single grain. The simulation result is used in the selecting of the processing parameters subsequently. Finally, a fixed soft abrader grinding-polishing experiment of sapphire single crystal substrate is presented, On the basis of the physical and chemical properties of the sapphire single crystal and the production technology of the fixed soft abrader disc, the fixed soft abrader disc was finished by recipe design technology, mixing technology etc. The effects of grinding pressure, grinding plate rotational speed etc on surface roughness and material removal rate (MRR) are analyzed; The result indicates that there is no pit and score in the face of the sapphire single crystal. It is the expected result.