Long-span dome structures are widely used for public assembly venues because of their large column-free space and efficient use of materials. When occupied by hundreds or even thousands of people, it would be devastating if they fail or collapse, which unfortunately happen frequently during extreme events, especially under tornadic winds. Although static effects of tornadoes on civil structures have been extensively studied, their dynamic impact has not been sufficiently investigated. In this study, non-stationary characteristics of tornadoes and their dynamic impact on a long-span dome structure are systematically investigated. In particular, the time-variant wind pressure on the dome surface induced by translating tornadoes with different intensities is characterized through Computational Fluid Dynamics simulations. The obtained wind pressure is then mapped onto the finite element model of the dome structure, and transient time-history analyses are conducted to characterize the tornado-induced dynamic responses. It is observed that non-stationary wind pressure and the induced dynamic structural responses are significant, when core radius of the tornado approaches the dome. Wind flow of EF4 and EF5 tornadoes is found to be more turbulent than EF2 and EF3 tornadoes, and hence larger and more rapid fluctuations of dynamic responses.