To realize efficient ultra-precision polishing of concave spherical optical glass with small curvature， a hemispherical head polishing device based on magnetic compound fluid （MCF） with a high apparent viscosity and stable distribution is proposed. First， the magnetic-field distribution of three different magnetic sources （axial magnetized cylindrical permanent magnet with a planar iron board and concave iron board installed above it） is simulated with the use of ANSOFT Maxwell. It is found that the addition of the concave iron board can strengthen the corner effect， and the magnetic field can be more concentrated. The dimensions of the magnetic sources and magnet eccentricity are optimized according to the simulation results. Second， by observing and comparing the behavior of the MCF slurry with different compositions and magnet eccentricities on the polishing head， the composition of the MCF slurry and magnet eccentricity are determined. Finally， a polishing experiment is performed on the concave spherical K9 glass workpiece with a curvature radius of 15.4 mm and center depth of 2.24 mm using the optimized polishing solution and self-made polishing device. Following 90 min of polishing， the root-mean-square （RMS） of the workpiece surface is reduced from 0.719 μm to 11.7 nm， and the surface roughness （R_a） is reduced from 0.552 μm to 9.656 nm. It is verified that the designed polishing device can achieve efficient nanoscale polishing of concave spherical workpieces with small curvature.