Axial turbines are gaining prominence in supercritical carbon-di-oxide (S-CO2) Brayton cycle power blocks. S-CO2 Brayton cycle power systems designed for 10 MW and upwards will need axial turbines for efficient energy conversion and compact construction. The real gas behavior of S-CO2 and its rapid property variations with temperature presents a strong challenge for turbomachinery design. Applying gas and steam turbine philosophies directly to S-CO2 turbine could lead to erroneous designs. Very little information is available in the open literature on the design of S-CO2 axial turbines. In this paper, design of a 10 MW axial turbine for a simple recuperated Brayton cycle waste heat recovery system is presented. Three repeating stages with nominal stage loading coefficient of 2.3 and flow coefficient of 0.37 were designed. An axial turbine mean-line design method tuned to S-CO2 real gas fluid medium is discussed. 3D blade design was made suing commercial turbomachinery design software AxSTREAM. The turbine was designed for inlet temperature of 818.15 K, pressure ratio of 2.2, rotational speed of 12000 rpm and mass flow rate of 104.5 kg/s. 3D CFD simulations were carried out using the commercial RANS solver ANSYS CFX 2020 R2 with SST turbulence model for closure. S-CO2 was modelled as real gas with Refrigerant Gas Property tables generated over the appropriate pressure and temperature ranges using NIST Refprop database. CFD studies were carried out over a range of mass flow rates and speeds, covering the design and several off-design conditions. The performance maps generated using 3D CFD simulations of the turbine are presented. The geometrical parameters obtained with the mean-line design matched well with that of the 3D turbine design arrived using AxSTREAM. It was observed that the turbine produced 10 MW power at the design condition while passing the required mass flow. CFD studies also showed that the preliminary turbine design achieved a moderate total-to-total efficiency of 80 % at the design condition. The design has potential for further optimization to obtain improved efficiency and for reducing the number of stages from three to two.