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To achieve the nano precision surface quality of LBO crystal, the fixed abrasive polishing technology was adopted to realize the nano machining process. The machining tool plays a key role in nano machining process and the same as the fixed abrasive polishing pad (FAP) for the polishing process. The effect of the matrix hardness and polishing powder concentration of the FAP on material removal rate, surface topography, microscopic appearances and surface roughness were investigated in nano machining LBO crystal. The results show that the matrix hardness B and the concentration of the polishing powder 150% of FAP are the optimization characteristics for the maximum material removal rate and the best surface quality in fixed abrasive polishing of LBO crystal. The maximum material removal rate is 71.4nm/min and the optimal surface roughness Sa is 0.657nm. The nano precision surface quality with nanoscale material removal was obtained in nano machining LBO crystal.