Organic Rankine cycle (ORC) is a promising method to convert low-grade thermal energy to electricity. The working fluid and the expander are two decisive factors of the ORC performance. This paper systematically presents the thermodynamic design of the supercritical organic Rankine cycle (SORC) and the aerodynamic design of its radial turbine for high temperature applications. The siloxane MM with high comprehensive properties is chosen as the working fluid. The performances of SORC with MM under different turbine inlet conditions are analyzed. Due to the high pressure ratio of the optimized SORC, a two-stage radial turbine is selected and the design procedure of its first stage is presented explicitly, including the preliminary 1D analysis and 3D CFD simulations at both nominal and off-design conditions. The numerical simulation performed by ANSYS-CFX provides satisfactory results compared to the meanline analysis. The total to static efficiency of the SORC radial turbine is 80.84% at the nominal condition with the pressure ratio of 6.86 and the rotational speed of 23,000rpm. The proposed radial turbine could effectively handle a relatively large variation of the pressure ratio with slight performance degradation at the nominal rotational speed.