The work aims to analyze the dynamic response characteristics of a fuel transport cask under multi-process sequential impact scenarios required by related national standards to support the structural safety design and the protective technology for the cask. Firstly, multi-process sequential impact tests on the cask were conducted regarding to four accident scenarios, i.e., lateral drop at 1.2 m height, steel rod penetration at 1 m height, 500 kg weight impact at 9 m height, and puncture at 1 m height, etc. and then the corresponding finite element simulations considering impact damage accumulation were conducted integrated with the experiments. The dynamic response characteristics of fuel transport cask under the sequential impact condition of four accident scenarios were analyzed in detail. Related analysis showed that the simulation results agreed well with the experiment results, and thus the correctness and practicality of finite element simulation approach with cumulative impact damage were verified. Both the test results and numerical simulation results showed that the buffer structure of the cask played a very good role in protecting the fuel components under the condition of excessive penetration impact, and the structure and function remained intact. The fuel transport cask has good cushioning performance and can meet the protection requirements under the multi-process sequential impact condition. The impact damage accumulation finite element simulation method can accurately analyze the dynamic response characteristics of complex structures under multiple sequential impact conditions, and has good practicability.