A stable and efficient element-free Galerkin method is proposed for steady convection-diffusion problems.In the method integrations are computed with a local Taylor expansion nodal integral technique.According to convection-dominated degree,integration nodes are adaptively shifted opposite to the streamline direction.Compared with conventional element-free Galerkin method with stabilization,the method exhibits better stability and higher efficiency in solving convection-dominated convection-diffusion problems.It is a pure meshfree method,which is independent of background integral.Moreover,the method is easy to be implemented.