Ductile damage model has been widely regarded as a valuable method to predict the failure of sheet metal. Based on the thermodynamic theory and continuum damage mechanics, the fully coupled ductile damage model can be developed, which also can better predict the initiation and growth of the fracture. But the identifications of model parameters with theoretical methodology are difficult due to the complex coupling relationships existing among all state variables. The inverse methodology is regarded as a good method to resolve the problem. In this paper, the recently proposed fully coupled ductile damage model is chosen to investigate the deformation behavior of DP600 steel, in which the mixed saturation isotropic and kinematic hardenings are taken into account and fully coupled with the ductile damage. During the identification process, the least square formula of the error between experimental and numerical results is selected as the target function. The trust region algorithm and genetic algorithm are used with the help of MATLAB for the identification of three damage parameters. Finally, by comparing the experimental and numerical results, the validations of two algorithms are proved. The efficiency of the optimization process with trust region algorithm is higher, but with lower accuracy. Meanwhile, the optimization process is greatly affected by the chosen initial values of the ductile damage parameters.