Optical and electronic industries are using lapping and polishing processing as a final finish rather than grinding, because they need more accurate parts of brittles non-metallic materials such as single crystals. Sapphire has been ground by the ultra-precision surface grinder having a glass -ceramic spindle of extremely-low thermal expansion with various cup-type resinoid-bonded diamond wheels of #400-#3000 in grain size. Sapphire can be ground in the ductile mode. And also, the surface roughness and grinding conditions has been clarified. The smooth surface of Sapphire less than 1nm RMS, 1nm Ra can be obtained by the ultra-precision grinding without any polishing process.