Abstract: The damage and cracking behavior of concrete is a trans-scale phenomenon since the macroscopic fracturing is greatly affected by the material structure on the mesoscale. How accurately and efficiently to simulate the trans-scale evolution process of concrete failure is still an open issue. In this work, an adaptive macro-meso-scale concurrent finite element (FE) based approach of concrete is proposed, in which concrete is considered as homogeneous in the elastic regime and as heterogeneous in the nonlinear regime. The macroscale and the mesoscale FE model should be parallelly generated for the whole analysis domain with a strategy of dual mesh containing both macroscale and mesoscale meshes. By defining an adaptive criterion of the scale transformation from macroscale to mesoscale, the macro-meso-scale concurrent model is adaptively updated depending on the stress status of the macroscale element. The shape function interpolation based a multi-point constraint method is adopted for the connection between the macroscale mesh and the mesoscale one. Numerical examples demonstrate that the proposed approach can reach a proper balance between the simulation precision by considering the mesoscale material structure of concrete and the efficient simulation by adaptively determining the mesoscale analysis region.