The main objective of the thesis is to analyze the potential for improving the aerodynamic efficiency of Siemens SGT5-2000E turbine section by optimizing the blade shapes. An adjoint-based shape optimization is implemented at the mid-span of the axial turbine. The optimization is performed, for the stator and the rotor individually, to reduce the entropy generation (objective function) with mass flow rate as the constraint. The design optimization methodology is implemented using SU2, an open-source computational fluid dynamics (CFD) tool coupled with the adjoint-based optimization technique. The SU2 optimizer algorithm begins by computing the objective function of the existing design by using the flow solver. The flow simulation is performed by solving the RANS equations and SST turbulence model. The discrete adjoint solver utilizes the objective function and constraints to evaluate the gradients of the objective function with respect to the design variables. Each of the design variables is altered to improve the shape and the gradients are used to find an optimal search direction. The algorithm is structured to iterate until an optimal shape is determined. The optimization methodology is implemented for the existing stator to reduce the entropy generation and an optimal shape is determined. Then, the rotor is optimized with the outlet conditions of the optimized stator as the inlet conditions. The optimized stator and rotor resulted in a significant decrease in entropy generation of about 16% and 24% respectively. Finally, with the optimized blades the stage simulation is performed which resulted in 1.4% increase in the total-to-total efficiency compared to the baseline stage.