The adaptive p-version finite element method is combined with bi-directional evolutionary structural optimization（ BESO） for the influence of calculation accuracy on the optimization result in the topology optimization process. According to the error control parameter setting,the element order is improved adaptively through the element energy error analysis,which effectively improves the finite element calculation accuracy,and the sensitivity filtering algorithm and the stabilization strategy are adopted to mitigate the checkerboard and iterative oscillation phenomenon. The feasibility of the method is verified by the example calculation of the minimum compliance topology optimization problem,the results show that the proposed method can improve the accuracy of topology optimization under rougher meshes,and obtain higher optimization efficiency and better optimization results.