In this paper, the effects of reactant type, abrasive concentration, reactant concentration and matrix hardness on friction coefficient, cross-sectional area of wear mark and roughness at wear mark were studied by single factor experiments of fixed abrasive ball grinding with KDP crystal. The test results show that: KHCO3 fixed abrasive ball has good symmetry of the wear scar, small roughness value at the wear scar, and small damage depth of KDP crystal. The cross-sectional area of wear scar increases with the increase of the concentration of abrasive and reactants, and decreases with the increase of the hardness of the matrix. The roughness at the wear scar decreases and then increases with the increase of the concentration of abrasive and reactant, and first increases and then decreases with the increase of the hardness of the matrix. The friction coefficient is not significantly influenced by the concentration of abrasive and reactants, but decreases with the increase of the hardness of the matrix. The abrasive scar contour symmetry is good and the roughness value at the wear scar is low when the composition of fixed abrasive ball is KHCO3 as the reactant, Ⅰ matrix, the abrasive concentration is 100% of the matrix mass, and the reactant concentration is 15%. The fixed abrasive pad was prepared from the components above, and the KDP crystal was polished by the pad. High efficiency and high precision machining can be achieved with surface roughness Sa of 18.5 nm and material removal rate of 130 nm/min.