Provided is a method for polishing a single crystal substrate composed of gallium nitride GaN, which is a material that cannot be processed easily, by a CMP process with satisfactory polishing efficiency and satisfactory polishing performance. In the polishing by a CMP process, the surface of a single crystal substrate composed of gallium nitride GaN is polished using an abrasive-grain-containing polishing pad in the presence of an acidic polishing solution. In this manner, high polishing efficiency can be achieved properly while keeping the surface roughness at a low level. The polishing solution is an acidic polishing solution having an oxidation-reduction potential ranging from Ehmin mV (wherein Ehmin is a value determined in accordance with formula (1)) to Ehmax mV (wherein Ehmax is a value determined in accordance with formula (2)) and a pH value of 0.1 to 6.5. (1) Ehmin (mV) =-33.9pH + 750 (2) Ehmax (mV) = -82.1pH + 1491