The existing thermal neutron molten salt reactor design has a complicated online processing system that has many technical difficulties. A thorium-based molten salt fast energy amplifier (TMSFEA) driven by a proton accelerator can operate stably for nearly 40 years at a rated thermal power of 300 MW without online processing. In order to simplify the core structure of TMSFEA, the core design is based on a hollow and moderator-free cylindrical geometry. The molten salt in the core serves as both fuel salt and spallation target. In this paper, based on the previous TMSFEA core neutron physics design, the core thermal-hydraulic design principles of TMSFEA are proposed, and a detailed core design with specific core structures as well as three-dimensional core thermal-hydraulic performance are obtained. Through computational fluid dynamics steady-state analysis, the arrangement of the core inlet and outlet and the shape of the core sidewall are optimized. Suitable distribution plates and skirt plates are proposed, and two corresponding lower plenum structures are designed to improve the flow field in the core. This study provides TMSFEA with core structures that meet the thermal-hydraulic design principles and also provides ideas for similar hollow reactor core designs.