<p>Commonly, the fine grinding requires a smaller grit size. With the development of electrochemistry, it has gradually achieved fine grinding with a larger grit size. To further apply the ELID (Electrolytic in-process dressing) grinding technology, a prototype of the circumferential swinging mechanism is established. In this study, it innovatively proposes a discrimination matrix method which makes the traditional grinding model reasonably incorporate the circumferential swinging feeding aspects. A variety of grinding forms could be described by the transformation of the discrimination matrix. For example, the unidirectional circumferential swinging feeding can be described by an upper triangular discrimination matrix or a lower triangular discrimination matrix. The chip sectional area and chip length have been derived considering the influence of the circumferential swinging mechanism. The surface topography predicting model is established, which is visually exhibited by the evolution of the ground-surface profile and the consecutive-cutting-edges profile. Verifications were carried out with various swinging amplitudes and swinging velocities. When the discrimination matrix is in the form of a diagonal matrix, the model will be simplified for the cut-in grinding. Although there are unexplored areas of the Pt values when the swinging angles fall somewhere between 0° and 10°, most of the results could accurately predict the variation of the surface Pt values generated under the circumferential swinging mechanism.</p>