Built upon the acoustic impedance of circular apertures and cylindrical cavities as well as the principle of electroacoustic analogy, an impedance model is developed to investigate theoretically the sound absorption properties of graded (multilayered) cellular metals having semi-open cells. For validation, the model predictions are compared with existing experimental results, with good agreement achieved. The results show that the distribution of graded geometrical parameters in the semi-open cellular metal, including porosity, pore size, and degree of pore opening (DPO), affects significantly its sound absorbing performance. A strategy by virtue of the genetic algorithm (GA) method is subsequently developed to optimize the sound absorption coefficient of the graded semi-open cellular metal. The objective functions and geometric constraint conditions are given in terms of the key geometrical parameters as design variables. Optimal design is conducted to seek for optimal distribution of the geometrical parameters in graded semi-open cellular metals.