Abstract: The structural materials in the reactor and the corrosion products in the loop will be activated into radionuclides after being irradiated by strong neutrons. These nuclides and their decay products are the main sources of radiation hazards for workers. Therefore, the efficient and accurate calculation of the inventory of these radionuclides is of great significance for the design of reactor shielding protection, radioactive source items and waste management. In this paper, the neutron activation calculation method based on the mini-max polynomial approximation (MMPA) method was studied. Compared with the traditional neutron activation calculation methods such as the transmutation trajectory analysis method and exponential Euler method, MMPA method has the advantages of good numerical stability, high efficiency and no need to deal with short-lived nuclides alone. Furthermore, two solution strategies based on the MMPA method were studied for activation calculation, including the direct inversion solution strategy and the iterative solution strategy. The first solution strategy was proposed by Yosuke Kawamoto. This solution strategy completed the solution of the nuclide density by directly inverting the coefficient matrix and then calculating the multiplication and addition of multiple matrices. This solution strategy was computationally inefficient because it involved matrix inversion operations and a large number of matrix and vector multiplication operations. Therefore, a second solution strategy was proposed to improve the computational efficiency of the MMPA method. This solution strategy firstly transformed the solution expression of the MMPA method into an iterative expression after appropriate transformation, then obtained the substitution matrix for each iteration based on LU decomposition, and finally completed the solution of the nucleon density by adding multiple matrices. Compared with the first solution strategy, the solution strategy avoids the direct inversion of the matrix, and effectively reduces the number of multiplications of the matrix, so it has higher solution efficiency. Based on the self-developed nuclide inventory calculation code AMAC, the two solution strategies of MMPA method were completed. The correctness of MMPA method applied to neutron activation calculation under multiple conditions was preliminarily verified by typical material activation examples and self-constructed large-scale coefficient matrix examples under irradiation conditions, decay conditions and pulse conditions. The test results show that the calculation results of MMPA method are in good agreement with the calculation results of each reference solution, and the calculation accuracy is equivalent to that of 16 order Chebyshev rational approximation method (CRAM). In terms of computational efficiency, the solution efficiency of the iterative calculation strategy based on MMPA proposed in this paper is significantly higher than that based on direct inversion. The computational efficiency of this calculation strategy is equivalent to that of 16 order CRAM. The MMPA method is feasible in neutron activation calculation, and has good calculation accuracy and high calculation efficiency.