Inverse design as an efficient way, is an attractive shape design method. In this method, the geometry is determined for a prescribed flow character such as velocity or pressure distribution. In this thesis, the diffuser of a centrifugal compressor is inversely designed with Ball-Spine Algorithm in order to improve its performance. The inverse design method integrates Ball-Spine Algorithm as a shape modifier and Ansys-CFX software as a quasi-3D flow solver. Shape modification algorithm and Ansys-CFX software are integrated in two ways. First, Ball-Spine equations are written inside the CFX as expressions. Therfore, both shape modification and flow solving is done by CFX. Next, shape modification is done by Matlab software. Matlab helps to link Ball-Spine equations and Ansys-CFX as flow solver. So the geometry should be meshed for each iteration. Consequently, geometry filtering at each iteration is provided and convergence rate increases. Performance of the diffuser of the centrifugal compressor is improved in two separate steps. At the first step, the axsisymmetric 90-degree bend duct between the radial and axial diffuser of the centrifugal compressor is modified with Ball-Spine Algorithm. For this purpose, performance of bend duct in swirling viscous flow regime is numerically obtained. Then Ball-Spine Algorithm is developed for swirling viscous flow regime and the effect of viscosity, swirl velocity (tangential velocity component) and initial guess geometry is studied. 90-degree bend duct is inversely designed with Ball-Spine Algorithm in swirling viscous flow regime to increase the pressure recovery coefficient. Results show that the convergence rate and stability of Ball-Spine Algorithm is desired for designinig ducts in swirling viscous flow regime. The pressure recovery coefficient of the axsisymmetric 90 degree bend duct increases up to about 7%. At the second step, the radial diffuser is omitted. Consequently, the diameter of engine is reduced and the engine weight is decreased. At this situation, the 90-degree bend duct is directly placed right after the impeller and guide vane is used at the bend duct path. The 90-degree diffuser is inversely designed with Ball-Spine Algorithm and consequently pressure recovery coefficient increases and secondary flow reduces. In the 90-degree diffuser, flow angle distribution is controlled at outlet of the duct and engine diameter is reduced about 24%. Keywords: Inverse design, Ball-Spine algorithm, Axsisymmetric 90 degree bend, Swirl viscous flow