In view of the conceptual design optimization problem of solid rocket motor (SRM) that takes the optimal range of aircraft as the objective, the geometric parametric models of grain, combustion chamber, and nozzle of complex three-dimensional motor as well as the performance models of thrust and mass were firstly established under fixed-scale constraints. Meanwhile, considering the harsh flight environment and high performance requirements of boost-glide aircraft, a multi-constraint range capability evaluation model was proposed. Then, the maximum range of aircraft corresponding to the current motor scheme was evaluated by adaptive Legendre-Gauss-Radau pseudo-spectral method, and a constrained mixed-integer parameter optimization problem was constructed. In order to solve the high time-consuming of the mixed-integer parameter optimization problem, the Kriging surrogate model was introduced, and the sequential approximate optimization algorithm for real number was adjusted by adding integer constraints. For slow convergence rate of the traditional global sampling criterion, a local enhancement strategy was proposed and verified numerically. Simulation results show that the flight trajectory obtained by the improved adaptive pseudo-spectral method satisfied all the constraints, and the optimized maximum range was increased by 12.89% compared with the original SRM scheme. The solution of the proposed algorithm was consistent with that of genetic algorithm, but the number of time-consuming function calls was only 2% of the genetic algorithm. Compared with the traditional sequential approximate optimization algorithm, the proposed algorithm had global search capability, and effectively improved the convergence rate.