A process of manufacturing a single-crystal silicon-carbide substrate, includes contacting a surface of a single-crystal silicon-carbide plate with a surface of a polishing pad; and moving the surface of the single-crystal silicon-carbide plate relative to the surface of the polishing pad while supplying a polishing solution to the surface the polishing pad, to polish the surface of the single-crystal silicon-carbide plate. The polishing pad comprises a non-woven fabric or a porous resin. The polishing solution comprises an oxidizing agent which comprises a transition metal having oxidation-reduction potential of 0.5 V or more. Neither the polishing pad nor the polishing solution comprises an abrasive.