Abstract: The conversion of complex geometric objects represented by triangular meshes into parametric surfaces is a critical issue in the design of CAD geometric engines. For a triangular mesh model with a coarse quadrilateral partitioning structure, this paper proposes a parameterized surface reconstruction method based on the Powell-Sabin subdivision. This paper first employs the mean value parameterization method to establish a mapping from each coarse quadrilateral structure M_T to the parameter domain D, and simultaneously obtains the triangular partitioning △ of D. Then, a single Powell-Sabin subdivision is applied to △ to achieve a refined triangular partitioning △^S. Moreover, using the geometric information of M_T, an interpolation function S is constructed in the bivariate spline space S（△^S）. After uniform sampling of D, S is used to approximate regular-valued points as surface points of the parametric surface. Lastly, by establishing an energy function with smoothness properties, the control point grid of the bicubic B-spline surface is solved to complete the surface reconstruction. Experiments present the reconstruction results of basic surfaces like cylindrical and saddle surfaces, as well as freeform surfaces like human head models. Numerical results indicate that, compared to adaptive algorithms, the proposed method can capture the geometric details presented by the given triangular meshes, reducing the MSE of vertex distances in complex model reconstruction by 38%.