Based on the characteristics of solid magnetic abrasive and abrasive flow finishing, a new technology of viscoelastic magnetic abrasive finishing is presented. The theoretical micro model of viscoelastic magnetic abrasive tools is established, and influencing factors of a positive pressure are determined by force analysis. Finishing mechanism of micro-grinding, slipping, rolling and so on is analyzed theoretically and verifying experimentally. Experiments also show that all burrs are removed, the edges are rounded off and the surface is smooth, the surface roughness value Ra of hole surface drops from 0.53μm to 0.05μm. Its successful application will effectively solve the practical difficulty of deburring and surface finishing for special shapes such as groove, keyway, etc., and fulfil the quantitative finishing of complex surfaces. Results can provide the theoretical basis for the preparation of viscoelastic magnetic abrasive and further experimental study of this process