In order to overcome the defects of conventional magnetorheological finishing (MRF) processes that are unable to finish small curvature radius concave surfaces of diameter within 10 mm, a novel precision MRF process using small ball-end permanent-magnet polishing head with a diameter of 4 mm is proposed in this paper. And experimental setup of a four-axis linkage MRF machine tool is fabricated. Magnetostatic simulation of the distribution of magnetic flux density indicates that the magnetic field uniformity of produced polishing head is 93.3 %. Magnetizing force analysis is done to analyze the formation of magnetorheological fluid in finishing region. In addition, the suitable range of C-axis angular position for finishing is generated to be 60°~70°. Finishing experiments on both nonmetallic and metallic specimens with different surface shapes have been conducted. The ability of the developed method of finishing process to improve surface characteristics of a workpiece is demonstrated to reach the surface roughness of finished surfaces below Ra 6 nm. It confirms that the present MRF process is capable of improving surface quality and performing the nanofinishing on small curvature radius concave surfaces.