Exhaust nozzle is one of the key components of pulse detonation rocket engine (PDRE). Exhaust nozzle can be used to improve the propulsion performance of PDRE. Method of characteristic (MOC) was used to calculate one-dimensional CJ(Chapman-Jouguet)detonation wave propagating in the ideal detonation tube. The unsteady blowdown process after the CJ detonation wave reach the exit of detonation tube was two-dimensional axisymmetric numerical simulated. The results of numerical simulation demonstrated the development of the unsteady flow field, and the unsteady waves and vortexes were discussed. Contrary to PDRE without nozzle, the CD nozzle can augment propulsive performance by 18.24%.