Glass and ceramic aspherical mirrors used as optical element s in a space astronomical observatory must be machined with very high profile accuracy and surfa ce smoothness. Precision grinding processes are very effective in fabrication of su ch profiles. In particular, with the ELID (Electrolytic In-Process Dressing) grinding method, it is possibl e to achieve ultraprecise and smooth surfaces of hard and brittle materials. To obtain the ultra smooth s urfaces, a final polishing process which requires a long processing time after the conventional grindi ng process is necessary. The ELID grinding method using an ultraprecision grinding machine tool with a nano-level hydrostatic guide will be very effective in reducing the time required for the finial polishing process. In this paper, a new ELID grinding system is introduced and the experimenta l r sults of fabricating a glass-ceramic paraboloidal mirror are presented and discussed. The profil accuracy of the fabricated glass-ceramic mirror was found within 0.54 m P-V.