In this research, one-dimensional design of centrifugal compressor with inverse design of 90-degree bend duct between radial and axial diffuser is accomplished using an iterative method and three-dimensional numerical simulation. In this study, the centrifugal compressor is designed by different parts as follows: an impeller, a vaned radial diffuser, a 90-degree bend duct and an axial diffuser. 1-D design is done with the following specified terms: mass flow rate, inlet stagnation pressure and temperature, inlet hub diameter of the impeller, shaft rotational speed and stagnation pressure ratio of the whole centrifugal compressor. Gas dynamics governing equations are obtained from working conditions. In design procedure, the geometrical dimensions of the compressor such as, impeller and diffusers inlet and outlet diameters, blades angles, vanes width, impeller and diffusers length, radius of curvature of 90-degree bend duct and some other geometric properties are calculated by a computational code. During design procedure, the actual pressure rise coefficient of the radial and axial diffusers and the axial diffuser outlet velocity are considered to be a function of the radial ratio and vanes numbers of the radial diffuser. The optimum design point is obtained under some constraints in a way that radial and axial diffusers pressure rise coefficient should be less than 0.7 and the axial diffuser outlet velocity should be 60 to 100 m/s. To evaluate the results, the geometrical dimensions calculated from 1-D design code are considered as an input data for blade generation using BLADE GEN software. Then, 3-D flow field in the impeller and two diffusers are analyzed numerically using CFX flow solver with SST turbulence model. Then, the compressor performance is obtained in design point conditions. The numerical simulation shows there is a high loss region through the 90-degree bend between the radial and axial diffuser because of its high curvature. In order to reach a minimum loss in the 90-degree bend duct, the aerodynamic design of a axisymmetric 90-degree bend duct with rotating viscous flow is carried out using an inverse design method. At the first step of the aerodynamic design, the shape modification capability of the 90-degree bend duct is generated by linking up the Ball-Spine inverse design algorithm as a shape modification algorithm and CFX software as a flow solver. Then, the inner and outer walls are modified by improving the hub and shroud pressure distribution and applying it to the inverse design code. This method is an indirect one and starts with an initial guess. In this algorithm, the duct walls are simulated by hypothetical balls moving freely in the specified directions, called spines. The advantages of this shape modification algorithm are high convergence rate and performing as a black box. Thus, the algorithm can easily be combined with any efficient flow solver. Finally, to check the outcome of design process, the designed centrifugal compressor with the modified 90-degree bend duct is simulated by CFX software for 3-D numerical analysis. The results show that, the total pressure ratio and overall efficiency of the centrifugal compressor is increased about 3 and 4 percent, respectively. Keywords: Centrifugal Compressor, 1-D Design, Inverse Design, Internal Flow, Ball-Spine, 3-D Numerical Simulation.