This paper addressed the design of a new function of minimum creep rate and stress function as a part of the original research work for the development of a set of creep damage constitutive equations. Firstly, the experimental data about the minimum creep strain rate and a wider range of stress were collected from literature; Secondly, the existing typical functions were calibrated with the collected data and the result was not satisfactory; finally, a new minimum creep strain rate and stress function was proposed and calibrated over a wider range of stress, and it was found to be the best. This paper contributed to the development of creep damage mechanics theory and method, as well as to the creep damage mechanics in general.