Sequential approximate optimization method has shortcomings in several respects, such as surrogate model establishing and infill strategy at present. Basing on local density of sampling points, the influence volume concept which is inversely proportional to local density was introduced and then the optimal kernel width of radial basis function was obtained by means of total influence volume optimization, thus, the function approximation needs in sequential approximate optimization process under the conditions of different scales and heterogeneous samples were satisfied. Potential feasible region infill strategy was proposed and potential optimal strategy was applied together, both exploration and exploitation capacity of the algorithm were satisfied. Three-step convergence criterion was set up. The algorithm flow process of sequential approximate optimization was constructed. For Golinski reducer optimization problem,the global optimal solution was solved after calculating original model 42 times, which embodied the good global optimization capacity and searching efficiency of the algorithm. Shape optimization mathematical model was established for TH-II rocket, global optimal shape was gained after 165 times of original model calling using the proposed method. The design efficiency was increased greatly and TH-II rocket aerodynamic shape was proved reliable by flight testing.