Abstract: The recently developed consistent high order element-free Galerkin (EFG) method not only dramatically reduces the number of quadrature points in domain integration but also accurately passes the linear and quadratic patch tests, and remarkably improves the computational efficiency, accuracy and convergence of the standard EFG methods.On this basis, this work presents the h-adaptive analysis for consistent high order EFG method by taking advantage of the convenience of the EFG method in adding approximation nodes locally.The proposed method adaptively determines the region which needs nodal refinement according to the gradient of the strain energy density.The generation of the new approximation nodes is based on the multi-level local mesh refinement of the background integration mesh.The gradual transition between the regions with and without nodal refinement is also considered.The relative error of the strain energy in two successive computation is adopted as the stop-criterion of the adaptive process.The proposed adaptive meshfree method is applied to the analysis of stress concentration caused by geometry, external boundary loads and body forces.Numerical results show that the developed method is able to refine the region with high stress gradient adaptively and to generate reasonable distribution of approximation nodes automatically.In comparison with the existing adaptive schemes of the standard EFG method, the proposed method shows remarkable advantages on computational efficiency, accuracy and the smoothness of the resulting stress fields.In comparison with the consistent high order EFG method using uniform nodal distribution, the proposed adaptive method dramatically reduces the number of computational nodes.As a consequence, it significantly improves the computational efficiency and accuracy of the consistent high order EFG method for the analysis of problems with local high gradients such as stress concentration.