In this research an inverse design algorithm, called ball-spine algorithm (BSA) is developed on a 90-degree bend duct between the radial and axial diffuser of a centrifugal compressor with viscous swirling inflow to bend duct. The shape modification process integrates inverse design algorithm and a quasi-3D analysis code. For this purpose, Ansys CFX software, is used as flow solver and inverse design algorithm is written as a code inside it. Shape modification is accomplished for viscous and inviscid flow to check the effect of viscosity on convergence rate. Also, the effect of swirl velocity in shape modification process is investigated, by considering increased pressure as the target parameter. The algorithm reliability for swirling flow is verified by choosing different initial geometries. Finally, aerodynamic design of the bend duct with BSA is accomplished to reduce losses in 90-degree bend. Shape modification process is carried out by improving the current wall pressure distribution and applying it to the inverse design algorithm. Results show that convergence rate and stability of BSA are favorable for designing ducts with swirling viscous flow. So that, the pressure recovery coefficient of the 90-degree bend duct is 4%increased.