Abstract: To evaluate the structural reliability of solid rocket motor propellant grain subjected to sequential curing and cooling and ignition impact loads, a reliability evaluation framework integrating refined numerical simulation and Sobol global sensitivity analysis was proposed. The parameters of a damage nonlinear viscoelastic constitutive model were calibrated via viscoelastic tests, and a simulation method for the grain structure under sequential loads was developed based on the UMAT subroutine. The weight contributions of elastic modulus, pressure amplitude, and Poisson's ratio on equivalent strain were quantified via Sobol sensitivity analysis, and the grain structural reliability was calculated. The results indicate that, compared with a single ignition impact load, the maximum equivalent strain response under sequential loads rises relatively by 8.33%, and the maximum equivalent stress response rises relatively by 8.52%. Under such loading condition,propellant grain enters the nonlinear viscoelastic stage and forms damage. The first-order sensitivity index of Poisson's ratio reaches 0.882 through the Sobol method, far exceeding those of elastic modulus (0.089) and pressure amplitude (0.016). Compared with a single ignition impact load, the structure reliability under sequential loads relatively drops by 0.2%, while the failure probability is fourfold that under single ignition impact load.