A method for producing a precipitation strengthened Ni-based superalloy material having a component composition consisting of, in terms of % by mass: C: more than 0.001% and less than 0.100%, Cr: 11% or more and less than 19%, Co: more than 5% and less than 25%, Fe: 0.1% or more and less than 4.0%, Mo: more than 2.0% and less than 5.0%, W: more than 1.0% and less than 5.0%, Nb: 0.3% or more and less than 4.0%, Al: more than 3.0% and less than 5.0%, Ti: more than 1.0% and less than 2.5%, and Ta: 0.01% or more and less than 2.0%, and optionally, B: less than 0.03%, Zr: less than 0.1%, Mg: less than 0.030%, Ca: less than 0.030%, and REM: 0.200% or less, with the balance being unavoidable impurities and Ni, wherein, when a content of an element M in terms of atomic % is represented by [M], a value of ([Ti]+[Nb]+[Ta])/[Al]×10 is 3.5 or more and less than 6.5, and a value of [Al]+[Ti]+[Nb]+[Ta] is 9.5 or more and less than 13.0, the method comprising: a blooming forging step of performing a forging at a temperature range of from a solvus temperature Ts that is a solid solution temperature of the y' phase to a melting point Tm, and performing an air cooling to form a billet having an average crystal grain size of # 1 or more, an overaging thermal treatment step of heating and holding the billet at a temperature range of from Ts to Ts+50°C and then slowly cooling it to a temperature Ts' that is Ts or lower so that γ'-phase grains are allowed to precipitate and grow and to increase an average interval thereof, and a crystal grain fining forging step of performing another forging at a temperature range of from Ts-150°C to Ts and performing another air cooling, wherein Ts is from 1,030°C to 1,100°C, and wherein crystal growth is suppressed by the γ'-phase grains resulting from the overaging thermal treatment to result in an overall average crystal grain size of #8 or more after the crystal grain fining forging step, wherein the average crystal grain size is in each case the grain size number specified in JIS G0551: 2013. C: more than 0.001% and less than 0.100%, Cr: 11% or more and less than 19%, Co: more than 5% and less than 25%, Fe: 0.1% or more and less than 4.0%, Mo: more than 2.0% and less than 5.0%, W: more than 1.0% and less than 5.0%, Nb: 0.3% or more and less than 4.0%, Al: more than 3.0% and less than 5.0%, Ti: more than 1.0% and less than 2.5%, and Ta: 0.01% or more and less than 2.0%, and optionally, B: less than 0.03%, Zr: less than 0.1%, Mg: less than 0.030%, Ca: less than 0.030%, and REM: 0.200% or less, a blooming forging step of performing a forging at a temperature range of from a solvus temperature Ts that is a solid solution temperature of the y' phase to a melting point Tm, and performing an air cooling to form a billet having an average crystal grain size of # 1 or more, an overaging thermal treatment step of heating and holding the billet at a temperature range of from Ts to Ts+50°C and then slowly cooling it to a temperature Ts' that is Ts or lower so that γ'-phase grains are allowed to precipitate and grow and to increase an average interval thereof, and a crystal grain fining forging step of performing another forging at a temperature range of from Ts-150°C to Ts and performing another air cooling, wherein Ts is from 1,030°C to 1,100°C, and wherein crystal growth is suppressed by the γ'-phase grains resulting from the overaging thermal treatment to result in an overall average crystal grain size of #8 or more after the crystal grain fining forging step, wherein the average crystal grain size is in each case the grain size number specified in JIS G0551: 2013. <EOS>