In the field of neutron radiation, the problem of neutron spectrum unfolding has attracted much attention. The Bonner sphere spectrometer is often used for neutron spectrum detection, and the maximum entropy method can be used to analyze the neutron spectrum of the Bonner sphere spectrometer. Based on this principle, this paper establishes a simulation model including the Bonner sphere spectrometer with reference to the neutron shielding experiment in 2014. The simulation results of Monte Carlo method are used as the prior spectrum, and the maximum entropy deconvolution code (MAXED) based on the principle of maximum entropy is used for neutron spectrum unfolding. The effectiveness and accuracy of the method are verified by comparing with the literature data. By increasing the number of random particles in Monte Carlo method, multiple groups of prior spectrum with different accuracy are obtained. For different prior spectrum, the final spectral solution results can be statistically significant and the spectral solution results are effective. After comparison, the more accurate the prior spectrum is, the higher the accuracy of the final spectral solution results, indicating that it is important to obtain accurate Monte Carlo calculation results through appropriate variance reduction method, which can provide reference for subsequent research and experiments. In this paper, the GRAVEL method based on iterative algorithm is used to solve the neutron spectrum simultaneously, and the comparison of the calculation results of the two methods further proves the superior performance of the solution spectrum of the MAXED method.