The aging heat treatment process comprises the following steps that S1, the furnace temperature is increased to 1100-1160 DEG C, an Inconel 625 alloy is put in, heat preservation is conducted for (d * 0.6 + 30)-(d * 0.6 + 70) min, d is the straight product of the cross section of the Inconel 625 alloy, and the unit is mm; s2, the Inconel 625 alloy is taken out and put into water to be quenched, and the quenching water temperature ranges from 10 DEG C to 25 DEG C; s3, the Inconel 625 alloy subjected to primary quenching is put into the furnace at the temperature of 750 DEG C to 800 DEG C again, tensile stress is applied, heat preservation is conducted for 20 h to 40 h, and the stress level ranges from 100 MPa to 250 MPa; and S4, the Inconel 625 alloy is taken out, secondary quenching is conducted, and the quenching water temperature ranges from 10 DEG C to 25 DEG C. According to the method, the tensile stress is applied to the Inconel 625 alloy subjected to solution strengthening, creep aging heat treatment is conducted, the generation efficiency of the delta phase is improved, hundreds of and thousands of hours of heating is not needed, the practicability of the alloy is effectively improved, in the heat treatment process, due to application of the tensile stress, the forming speed of the delta phase is higher, the number of the delta phase is larger, and distribution is more uniform; the size is smaller, and the tensile strength is greatly improved.