In this paper a node enrichment-moving error estimate and adaptive refinement procedure in Mixed Discrete Least Squares Meshless (MDLSM) method is suggested to improve the solution of elasticity problems. The suggested method uses of two node enrichment and node moving refinement procedures simultaneity. The voronoi diagram is used to locate the position of new added nodes in enrichment step. The errors of new added nodes, after each enrichment procedure, are calculated via interpolation rather than the error of simulation nodes to reduce the computational effort. So, the additional simulation effort saves and the steps of suggested method and conventional enrichment procedure are same. Completing the enrichment step, a node moving procedure is used to improve the solutions and solving the nodes excessive vicinity problem that is happened in conventional node enrichment procedure, especially with irregular node distribution. The node enrichment-moving method is continued to obtain the desirable accuracy. The proposed method is used to solve several examples and the results are presented and compared with those of conventional node enrichment procedure and analytical exact solutions. The results show superior efficiency, effectiveness and accuracy of the proposed method compared to conventional node enrichment method.