Solid rocket motor design becomes a clamant task where fusion of design and non-design parameters may lead to various design configurations, especially under uncertainties. This paper proposes a robust design optimization method for the performance of a dual thrust solid rocket motor under investigation of the propellant burning rate and grain geometry uncertainties. It was found that due to uncertainties, the burning rate varies erratically during burning surface area regression, which may lead to catastrophic failure. The present approach aims at uncertainty quantification associated with burning rate and its influence on dual thrust motor performance. A first-order orthogonal design is applied to estimate the worst case deviation coupled with motor internal ballistics. The robustness assessment is measured directly by a mean-variance and average difference approach. A sensitivity analysis of performance parameters is performed to analyze the effects of variation of the design parameters. A hybrid genetic algorithm and simulated annealing approach is used as optimizer. The robust design solution obtained in the form of insensitive design and performance parameters shows the effectiveness and efficiency of the proposed methodology.