Fixed abrasive lapping and polishing (FALP) is a new machining technology and was adopted to manufacture hard brittle materials and obtain the high productivity because of fixed abrasive. The preparation process of fixed abrasive pad (FAP) was described. FALP of K9 glass, mobile panel glass and Si were investigated with fixed 5-10 µm diamond abrasives. The effect on material removal rate (MRR) and surface quality of different materials was studied. The results show that in the same FALP process conditions, Si is the highest MRR and reaches 4428 nm/min, mobile panel glass is inferior to and K9 glass is the lowest. And surface quality of mobile panel glass that surface roughness Sa is 2.10 nm and little and less damages is the best, Si is followed and K9 glass is the worst. So FALP can obtain the higher MRR and reaches several micrometers per minute and the better quality that surface roughness Sa can reach nanometer level for different materials.