A heating process is performed in a nitrogen atmosphere at a temperature of not less than 1650° C. upon an epitaxial substrate including a single crystal base and an upper layer made of a group-III nitride crystal and epitaxially formed on a main surface of the single crystal base. The result shows that the heating process reduces the number of pits in a top surface to produce the effect of improving the surface flatness of the group-III nitride crystal. The result also shows that the dislocation density in the group-III nitride crystal is reduced to not more than one-half the dislocation density obtained before the heat treatment.