The traditional finite element analysis for irregular design domains often encounters challenges such as intricate mesh discretization and inaccurate boundary description. In this paper, we propose a quadtree scaled boundary finite element method based on NURBS curves where the boundaries can be accurately represented. Quadtree decomposition, which satisfies the 2:1 rule, is employed to rapidly subdivide the analysis domain. The scaled boundary finite element method (SBFEM) is utilized to analyze the internal elements and address the displacement incompatibility issue of hanging nodes in the quadtree. Furthermore, the boundary element is discretized into boundary curves and internal lines, whose displacement fields are respectively constructed by the NURBS shape functions and the Lagrange shape functions, and then the subsequent analysis of the boundary element is completed by SBFEM. Finally, numerical examples are tested to demonstrate the feasibility of the proposed method, which effectively enhances computational efficiency and accuracy in solving irregular design domains.