Abstract: In this paper, an adaptive finite element (AFEM) method is designed by using the newest vertex bisection for linear elasticity problems in two dimensions. This method marks exclusively according to the error estimator without special treatment of oscillation and performs a minimal element refinement without the interior node property. Furthermore, a type of multigrid method based on the local relaxation is applied to the AFEM discrete systems by using the special properties during refinement. The results of various numerical experiments are shown that the proposed AFEM method is uniformly convergent and has quasi-optimal numerical complexity. The resulting multigrid method is much more robust and efficient in CPU times than the usual multigrid methods.