Damage plays an important role in nonlinear mechanical properties of quasi-brittle concrete materials. However, there are problems of grid sensitivity and zero energy consumption when local damage model is used in finite element method. At the same time, the traditional single mesh finite element model is difficult to treat the linear elastic region and nonlinear region of component in a different way, which can not focus the limited computation costs on the key areas. Through pre-setting high-precision finite element grids in local sub-domains and introducing inter-scale linear multi-point constraint methods, the concurrent multi-scale method and the total-finite element tearing and interconnecting method were combined. Meanwhile, the gradient-enhanced continuum damage model was applied to describe the nonlinear behavior of concrete. Furthermore, the dual assembly method was used to solve the large linear equations of the model. Then a concurrent multi-scale domain decomposition method was proposed for concrete failure analysis. The model was used to simulate the four-point bending test of a single notched concrete beam. Finite element meshes with three different precisions were generated for the pure bending regions where damage may emerge. The numerical results can reproduce the failure mode of concrete specimen, the model is reasonable and not mesh sensitive, which can provide a multi-scale numerical simulation technical support to explore the failure of concrete components with a clear damage pattern.