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A novel magnetorheological finishing (MRF) process using a small ball-end permanent-magnet polishing head is proposed, and a four-axes linkage dedicated MRF machine tool is fabricated to achieve the nanofinishing of an irregular ψ-shaped small-bore complex component with concave surfaces of a curvature radius less than 3mm. The processing method of the complex component is introduced. Magnetostatic simulation during the entire finishing path is carried out to analyze the material removal characteristics. A typical ψ-shaped small-bore complex component is polished on the developed device, and a fine surface quality is obtained with surface roughness Ra of 0.0107 μmand surface accuracy of the finished spherical surfaces of 0.3320 μm(PV). These findings indicate that the proposed MRF process can performthe nanofinishing of a kind of small-bore complex component with small-curvature-radius concave surfaces.