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The invention discloses an ultra-precise curved surface finishing method based on non-Newtonian fluid shear thickening effect. The method includes: adding abrasive particles or micropowder into non-Newtonian fluid with shear thickening effect to prepare non-Newtonian fluid polishing solution, wherein the non-Newtonian fluid accounts for 50%-90% of the mass of the polishing solution, the abrasive particles or the micropowder account for 10%-50% of the mass of the polishing solution, and the particle size of the abrasive particles or the micropowder ranges from 0.05 micrometer to 50 micrometers. Relative motion is generated between a workpiece and the polishing solution during polishing, shear thickening is generated at a contact portion of the polishing solution and the workpiece under shearing action, viscosity of the polishing solution in the contact area is increased to enhance holding force to the abrasive particles or the micropowder, and removal of workpiece surface materials is achieved under the micro cutting or chemical mechanical action of the adding abrasive particles or micropowder with polishing effect in the polishing solution on the workpiece, so that polishing of the workpiece surface is achieved. The ultra-precise curved surface finishing method based on the non-Newtonian fluid shear thickening effect can achieve efficient and high-quality polishing to various curved surfaces, in particular to complex curved surfaces and has great economic and social benefits.