A method for producing a ring-rolled material of an 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, optionally up to 0.35% of Si, optionally up to 0.35% of Mn, optionally up to 0.015% of P, optionally up to 0.015% of S, optionally up to 0.30% of Cu, and the balance of Fe with inevitable impurities, using ring rolling, the method comprising: an intermediate 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 rage 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; and a circularity correcting step of improving a circularity of a ring-rolled material that has been rolled by the finishing ring rolling 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 the ring-rolled material that has been rolled by the finishing ring rolling step is subjected to the circularity correcting step without being reheated, or the ring-rolled material that has been rolled in the finishing ring rolling step is subjected to the circularity correcting step in a temperature range of up to 960°C excluding a temperature range of 600 to 760°C. an intermediate 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 rage 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; and a circularity correcting step of improving a circularity of a ring-rolled material that has been rolled by the finishing ring rolling 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 the ring-rolled material that has been rolled by the finishing ring rolling step is subjected to the circularity correcting step without being reheated, or the ring-rolled material that has been rolled in the finishing ring rolling step is subjected to the circularity correcting step in a temperature range of up to 960°C excluding a temperature range of 600 to 760°C. <EOS>