Abstract: In the traditional finite element analysis,there is not a good approximation method for curved boundaries or the interface of curved edge,and a large number of linear elements are used to describe the computational domain of curved edges.These additional elements not only waste computing time,and often are not the necessary part to solve.To use curved element can avoid the force refinement of the elements and effectively improve the calculation accuracy.By using the non-uniform rational B-spline(NURBS) curve algorithm can effectively eliminate the geometric discretization error,and ensured the overall high continuity.This paper discusses adaptive triangular mesh generation and quadrilateral mesh generation based on the NURBS curves in detail and solves practical problems with hp-adaptive finite element algorithm.The results were compared from the degree of freedom and the computing time,the NURBS based hp finite element method can eliminate the errors caused by geometric approximation and improve the computational efficiency.