For studying and analyzing the mechanism and process of quick-point grinding deeply, the models and the parameters of the edge contact layer in the process are established based on the technical and geometrical characteristics of quick-point grinding. The equivalent speeds and diameters of the wheel and workpiece as well as the grinding parameters are analyzed in theory. On the basis of the works above, a formula considering the point grinding angles and the depth of cut is theoretically deduced to calculate the contact width in wheel edge, and numerical simulations are performed for the edge contact width of an ultra-thin grinding wheel and ground surface roughness in quick-point grinding. It is shown that the edge contact width is not always equal to the thickness of the wheel like conventional cylindrical grinding process, the point grinding angles and the depth of cut influence the edge contact width and surface roughness evidently in quick-point grinding process.