Dense buildings are the major factor affecting urban flood routing. Currently, the study of urban dam-break flood routing primarily focuses on a simplified terrain model and 2D shallow water equations, which ignore the effects of dense urban buildings. Furthermore, the complex interactions between the dam-break wave and the wall surfaces of buildings are not reflected in the results. To tackle these problems, three-dimensional flood routing with a high-precision digital model of an urban area is studied in this paper. Firstly, the vector data of various land types is extracted from a remote sensing image, and the NURBS algorithm based on the TIN algorithm is introduced to construct a three-dimensional terrain model. Coupled with the vector data and the terrain model, a three-dimensional digital model of the urban area is established. Next, a three-dimensional k-epsilon turbulence model is proposed for the flood routing simulation. A polyhedral grid with a second-order accuracy and a discrete format is used to divide the digital model of the urban area, and the governing equations are solved using the PISO algorithm. Finally, the superiority of the 3D mathematical model and the computational efficiency of the polyhedral mesh model are validated according to the urban flood routing experiments of Testa and Soares-Frazao. An urban reservoir, located in SZ City, China, is modelled to show that a dam-break flood in an urban area exhibits significant three-dimensional characteristics. Moreover, due to the surrounding buildings, the flood exhibits complex three-dimensional turbulence phenomena, including collision, reflection and vortices.