Abstract: The use of a non-local damage constitutive model in biomechanics of soft biological soft tissues has significant advantages in considering internal scale variables and in avoiding mesh-dependence in finite element simulations. There are very few researches on the inverse problems of non-local constitutive models in literatures. A numerical model for solving the non-local damage inverse problem is proposed, the advantages of which are: The constitutive parameters can be effectively identified by solving an inverse problem; The non-local unified damage-growth-healing coupled constitutive model is employed to conveniently considering the effect of internal length scale and establish governing equations of healing parameters; A surrogate model is used to replace the nonlinear finite element method based direct analysis to reduce the computational cost. The measurement information is provided by conducting in vitro tensile experiments and finite element simulations of bovine aortic soft tissue. The results of the numerical examples show that the method proposed has good computational accuracy and noise resistance. The curve fitting indicator with identified parameters for isotropic and anisotropic backpropagation calculations are 0.9879 and 0.9754, respectively. This article provides an effective numerical model for identifying damage constitutive parameters of soft tissue.