Supersonic Dual Bell Nozzle (SDBN) is an altitude-adaptive propulsion nozzle achieved only by a nozzle wall inflection. In order to investigate the altitude adaptive capability and the effectiveness of this nozzle concept, the present study addresses a computational work of the flow through SDBN. Several types of the SDBNs are tested for a wide range of the pressure ratio which covers from an over-expended flow to a fully under-expended flow at the exit of the SDBN. Axisymmetric, compressible, Wavier-Stokes equations are numerically solved using a fully implicit finite volume differencing scheme. The present computational results reveal that the base nozzle length affects the shock wave system occurring inside SDBN. For a quit wide range of the pressure ratio the flow separation occurs at the nozzle inflection point. It is found that the maximum thrust coefficient is obtainable for the correct expansion state at the exit of SDBN.