A method for producing a ring-rolled material of an Fe-Ni based superalloy having a composition including, by mass%, up to 0.08% of C, 50.0 to 55.0% of Ni, 17.0 to 21.0% of Cr, 2.8 to 3.3% of Mo, 0.20 to 0.80% of Al, 0.65 to 1.15% of Ti, 4.75 to 5.50% of Nb+Ta, up to 0.006% of B, and the balance of Fe with inevitable impurities, using ring rolling, the method comprising: a finishing ring rolling step, as a final step of the ring rolling, of heating a material for ring rolling in a temperature range of 900 to 980°C, and expanding a diameter of the material for ring rolling and also pressing the material for ring rolling in an axial direction thereof by using a ring rolling mill having a pair of rolling rolls including a main roll and a mandrel roll, and a pair of axial rolls; a heating step of heating a ring-rolled material that has been rolled by the finishing ring rolling step, in a temperature range of 980 to 1010°C; and a circularity correcting step of improving a circularity of the ring-rolled material that has been heated by the heating step, while expanding a diameter of the ring-rolled material by using a ring expander including a pipe-expanding cone and a pipe-expanding die, wherein in the circularity correcting step, a diameter expansion rate for an outer diameter of a ring of the ring-rolled material is up to 0.8%; and wherein the method further comprises an intermediate ring rolling step, as a pre-step of the finishing ring rolling step, of heating the material for ring rolling to a temperature range of higher than 980°C and up to 1010°C, and expanding a diameter of the material for ring rolling that has been heated at the temperature range and also pressing the material for ring rolling in an axial direction thereof by using a ring rolling mill having a pair of rolling rolls including a main roll and a mandrel roll, and a pair of axial rolls. a finishing ring rolling step, as a final step of the ring rolling, of heating a material for ring rolling in a temperature range of 900 to 980°C, and expanding a diameter of the material for ring rolling and also pressing the material for ring rolling in an axial direction thereof by using a ring rolling mill having a pair of rolling rolls including a main roll and a mandrel roll, and a pair of axial rolls; a heating step of heating a ring-rolled material that has been rolled by the finishing ring rolling step, in a temperature range of 980 to 1010°C; and a circularity correcting step of improving a circularity of the ring-rolled material that has been heated by the heating step, while expanding a diameter of the ring-rolled material by using a ring expander including a pipe-expanding cone and a pipe-expanding die, wherein in the circularity correcting step, a diameter expansion rate for an outer diameter of a ring of the ring-rolled material is up to 0.8%; and wherein the method further comprises an intermediate ring rolling step, as a pre-step of the finishing ring rolling step, of heating the material for ring rolling to a temperature range of higher than 980°C and up to 1010°C, and expanding a diameter of the material for ring rolling that has been heated at the temperature range and also pressing the material for ring rolling in an axial direction thereof by using a ring rolling mill having a pair of rolling rolls including a main roll and a mandrel roll, and a pair of axial rolls.