In development of large-scale astronomical telescopes, some new ceramics such as Silicon Carbides (SiC) and glass-ceramics (Zerodur) are applied for primary mirrors. However, the surface finish of the mirrors composed of the ceramics is time-consuming by traditional polishing method. In this study, ELID (Electrolytic In-process Dressing) grinding method, which could achieve high efficiency, was conducted to grind the ceramics for lightweight mirrors (CVD-SiC, Sintered-SiC, Zerodur). The properties of ELID grinding surface were investigated by AFM observation. The results demonstrate that on the ground surface of CVD-SiC and Zerodur, micro voids and micro cracks generated in rough grinding process can be eliminated by #4000 grinding wheel. The total depth of cut required is about 15, m. Another way, it is difficult to eliminate the micro voids and micro cracks generated on ground surface of Sintered SiC, even under condition of much less depth of cut.