We have developed a fabrication technique for narrow NbC/sub x/N/sub 1-x//MgO/NbC/sub x/N/sub 1-x/ junctions on MgO substrates using chemical-mechanical polishing (CMP) for the removal of SiO/sub 2/ insulation layer from the top of junctions. Parameters of CMP have been optimized so that the run-to-run deviation of removal rate for SiO/sup 2/ is less than /spl plusmn/20% and uniformity across a 10 mm/spl times/10 mm area is better than /spl plusmn/20%. Using the optimized CMP, NbC/sub x/N/sub 1-x//MgO/NbC/sub x/N/sub 1-x/ junctions with width of 1-4 /spl mu/m have been successfully fabricated. Fabricated junctions showed no superconducting leakage current and critical current densities of interconnections between the counter electrode and the wiring were larger than 1/spl times/10/sup 8/ A/m/sup 2/. This CMP-based fabrication technique is applicable to SIS mixers and Josephson local oscillators operated near 1 THz.