Abstract: In order to solve the time-consuming problem of high-fidelity neutron transport calculation, the multi-level acceleration theory was proposed. For iterative process, the iterative acceleration was utilized to ease the computational burden. An equivalent low resolution system with different spaces, energy and angular resolutions was built, forming the multilevel iterative acceleration. The solution of low resolution system can provide good initial value for high resolution system, so the number of iterations for high resolution system calculation was greatly reduced. For the purpose of ensuring the complete equivalence among different resolution systems, the generalized equivalence theory based coarse mesh finite difference method was used in iterative process. Aiming at transient solution, the timestep acceleration was adopted to decrease the calculating amount of highfidelity neutron transport by establishing a multilevel predictorcorrector system. Based on the idea of predictorcorrector, the time step of high-fidelity transient neutron transport calculation was divided into multiple levels. Meanwhile, the corresponding low resolution systems were established under different time resolutions, so as to effectively capture the characteristics of neutron flux density in different resolutions. Then the low resolution system result was used to adjust the predicted solution of high resolution system step by step, thereby achieving accurate highfidelity neutron transport calculation under large time steps. Ultimately, the concept of time, space, energy, and angular resolution system were introduced, and the timestep acceleration and iterative acceleration were integrated into a complete multilevel acceleration theory. Furthermore, the theory was applied to the highfidelity neutron transport program HNET and a specific implementation scheme was established, which includes four levels of acceleration in time step scale, three levels of acceleration in space scale, and two levels of acceleration in energy scale. The acceleration performance of multilevel acceleration theory was verified by the single assembly problem with a prompt control rod withdrawal event and the wellknown C5G7TD benchmark problems. The numerical results indicate that the computational accuracy of HNET program is comparable to that of the international sametype program. In addition, the efficiency is significantly better than that of the similar program. On the one hand, the multilevel iterative acceleration has the capability of enhancing the converge speed of high resolution system calculations. On the other hand, the multilevel predictorcorrector quasistatic method can provide accurate correction factor under large time step, making the improvement of calculation precision come true. In summary, the multilevel acceleration theory can not only ensure the accuracy of highfidelity neutron transport calculation, but also greatly improve the computing efficiency.