To establish a high performance supercritical carbon dioxide (SCO₂) Brayton cycle system, a two-stage SCO₂ axial turbine was designed for the 5MW supercritical carbon dioxide thermal power platform by using the self-compiled one-dimensional turbine design program based on the Denton loss model, AXIAL software and AXCENT software. RANS equations and SST Turbulence Model were chosen for numerical study on the aerothermodynamics performance of SCO₂ turbines in the design working condition and variable operating conditions using commercial software CFX and the real physical properties of SCO₂ from the NIST software. Simulation results indicated that the two stage axial flow straight cascade turbine scheme was selected in considering the realizability of the auxiliary system of the SCO₂ turbine with high design parameters. After the blade optimization, the total pressure loss of two rows of turbine stator blades is about 0.042, and the relative total pressure loss of the first and second rotor cascade were 0.050 and 0.064, respectively. The Mach number distribution of the root, middle and top flow field of turbine blades is reasonable. Considering the leakage and mixing loss of the stator and rotor blades, the isentropic efficiency of the SCO₂ high pressure turbine with the good variable operating performance can reach 84.88% and the shaft power of the turbine is 3 251 kW at the design point, which can meet the design requirements.