A cumulative damage model of solid propellant was established based on energy dissipation damage variable defining method and dynamic linear viscoelastic theory. The expression of dissipated energy when destroyed was obtained according to the experimental data of different stretch rates, and the formula of cumulative damage for grain was presented as well. Considering influence of circular stress magnitude and frequency, the rule of cumulative damage varying was researched respectively, and a case of cumulative damage and life prediction for solid rocket motor grain was analyzed finally. The method is beneficial for the storage life prediction of solid rocket motor.