Abstract: Yttrium aluminum garnet (YAG) is a kind of hard-brittle and difficult-to-machine material with wide application. Its polishing process is complicated and inefficient. Fixed abrasive polishing technology has the advantages of excellent planarization ability, high selectivity for workpiece surface morphology, and high abrasive utilization. The effect of matrix hardness and diamond particle size of fixed abrasive pad on material removal rate and surface quality was investigated in fixed abrasive polishing of YAG crystal. The results show that when the hardness of the matrix is moderate to Ⅱ and the diamond abrasive size is 3 to 5 μm, the effect of fixed abrasive polishing of YAG crystal is the best. Under these conditions, material removal rate is 255 nm/min and surface roughness S_a is 1.79 nm in fixed abrasive polishing of YAG crystal.