In this paper, the design algorithm of a second throat exhaust diffuser applicable in altitude tests of large expansion ratio nozzles is presented. In this algorithm, the geometric parameters of the exhaust diffuser are classified into primary and secondary parts. The primary geometric parameters are calculated from normal shock theory incorporating with a correction coefficient. However, the secondary parameters are selected from the previously reported experimental results. Numerical simulation tool is utilized to satisfy the design candidates and to finalize the correction factor. Axis-symmetric compressible Navier–Stokes equations incorporated with two equation Kω-SST turbulence model are solved to extract the supersonic exhaust diffuser flow features. As a first stage of numerical analysis, we use an unsteady pressure-based solver to accelerate the solution procedure. At the second stage, we use steady density-based solver to enhance the accuracy of our solutions. The current numerical method is properly validated by experimental reported results in the literature. Finally, we focused on simulation results of a designed diffuser and described the flow futures at different boundary conditions. The simulation results are confirmed that the designed diffuser is suitable for proposed altitude test.