Abstract: A mathematical model of a axisymmetric converging-diverging nozzle in design conditions is set up by quadratic-regression equation. The thrust force coefficient is taken as objective function. The three geometric parameters (half convergent angle, half-divergent angle, radias ratio of throat curvature to throat) are chosen as design variables. The optimum design is completed py the random-walk method. Then the relationships of the optimum geometric parameters to the designed pressure ratio of the nozzle are obtained. The results provide the basis for designing the axisymmetrie convergent-divergent nozzle of an exhaust system.