Ceramic-Al substrates with co-continuous ceramic and metal phases, which exhibit high thermal conductivity and compatible coefficient of thermal expansion (CTE), have been widely investigated through the process of die-casting. In this research, a kind of powder sintering process was proposed for fabricating ceramic-Cu composite substrates with co-continuous phases. Copper fiber (Cuf) has excellent thermal conductivity and large aspect ratio, making it an ideal material to form bridging network structures in the ceramic-Cu composite. To maintain the large aspect ratio of Cuf, and densify the composite substrate, ZnO-SiO2-CaO glass was introduced as a sintering additive. Both Al2O3/glass/Cu-f and Al2O3/30glass /Cu-p composite substrates were hot-pressed at 850 degrees C under 25 MPa. Experimental results showed that the thermal conductivity of Al2O3/30glass/30Cu(f) composite substrate was as high as 38.9 W/mK, which was about 6 times that of Al2O3/30glass; in contrast, the thermal conductivity of Al2O3/30glass/30Cu(p) composite substrate was only 25.9 W/mK. Microstructure observation showed that, influenced by hot press and corrosion of molten ZnO-SiO2-CaO glass, the copper fibers were deformed under hot-pressing, and some local melting-like phenomena occurred on the surface of copper fiber at 850 degrees C under 25 MPa. The molten phase originating from surface of Cu-f welded the overlapping node of copper fibers during cooling process. Finally, the interconnecting metal bridging in ceramic matrix was formed and behaved as a rapid heat-dissipating channel, which is similar to substrates prepared through die-casting process by porous ceramic and melted Al.