The slurry chemical action affects chemical reaction between the wafer and slurry, and self-conditioning performance of the pad in nano machining process. Fixed abrasive polishing, one of important nano machining technologies, was adopted to achieve a nano precision surface quality of CaF₂ crystal. Five kinds of alkaline regulators, triethanolamine, sodium citrate, sodium carbonate, ethylenediamine and sodium phosphate in slurries with pH 10, were screened in nano machining CaF₂ crystal. The effect on material removal rate (MRR), surface topography and surface roughness was investigated in fixed abrasive polishing of CaF₂ crystal. The results indicated that surface quality is getting better with MRR decreasing. The optimal surface quality of CaF₂ crystal with surface roughness Sa 4.13 nm can be obtained by sodium phosphate slurry with MRR 224 nm/min in fixed abrasive polishing of CaF₂ crystal. The nanometer precision surface quality with high material removal was achieved in nano machining CaF₂ crystal.