The rapid development of high-performance computer provides the hardware environment for high performance numerical simulations. Many numerical simulations have the ability of handling meshes from billions of elements to tens of billions. However, the development of parallel mesh generation, which is a critical step in numerical simulation, is relatively lagging behind. Thus, a multilevel parallel unstructured tetrahedral mesh generation algorithm for complex geometric models was presented. Firstly, a sizing-function of the mesh was established on the basis of the geometric features of the model, and the geometric entities were grouped on the basis of the sizing-function and the adjacency relationship between the geometric entities. The grouped geometric entities were distributed to different computing nodes. Then the triangular meshes were generated by the advancing front method among the nodes. And the triangular meshes were decomposed into sub-meshes which were distributed to each process. Finally, a multi-threaded parallel algorithm was used to generate tetrahedral meshes in the process. The proposed parallel mesh generation algorithm was validated on the Three Gorges Dam model, and the results show that the presented algorithm has good parallel efficiency and scalability, and can generate billions of high quality tetrahedral meshes for modern supercomputers with thousands of processor cores.