A method for producing a low thermal expansion Ni-base superalloy including the steps of subjecting the alloy to a solution heat treatment under the condition of at a temperature of 1000 to 1200° C. and subjecting the alloy to either a carbide stabilizing treatment for making aggregated carbides on grain boundaries and stabilizing the carbides under the conditions of at a temperature of not less than 850° C. and less than 1000° C. and for 1 to 50 hours, or a carbide stabilizing treatment for making aggregated carbides on grain boundaries and stabilizing the carbides by cooling from the temperature in the solution heat treatment to 850° C. at a cooling rate of 100° C. or less per hour. The method also including the steps of subjecting the alloy to a first aging treatment for precipitating y′ phase under the conditions of at a temperature of 720 to 900° C. and for 1 to 50 hours, and subjecting the alloy to a second aging treatment for precipitating A2B phase under the conditions of at a temperature of 550 to 700° C. and for 5 to 100 hours.