Abstract: The neutron transport equation is the primary equation for nuclear reactor physical analysis and calculation, which are usually solved by discrete ordinate (SN) method, method of characteristics (MOC), Monte Carlo method, and other numerical methods in tradition. In recent years, technical research on solving differential equations using deep learning methods has gradually become a cutting-edge hot topic in the field of numerical computation. Significant progress has been made in solving the differential equations. However, it is hard to solve the transport equation using deep learning methods directly. The main reason is that there are several multiple integral terms of angular flux density in the transport equation, which leads to the original method not being available. In order to address these challenges, the differential transform order theory of neutron transport equation was proposed in this work. The basic idea of this method is to transform the complex neutron transport equation with integral terms of angular flux density into a pure high-order differential equation. In the theory, the integral terms of the transport equation were transformed into their corresponding primitive function by mathematical method. Then, other terms of the neutron transport function were correspondingly expressed as a high-order differential form of the primitive function. Since the primitive function corresponding to definite integral is a multi-function family, the constraint conditions for determining the definite solution of the primitive function were provided. For different boundary constraints of the transport equation, the corresponding boundary condition forms represented by the primitive function were also proposed. The weighted loss function was constructed based on the constraints including the control equation, boundary conditions, constraints on the definite solution of the primitive function, and eigenvalue constraints. The deep learning method was used to make the artificial neural network approximate the primitive function. After the training, the derivative of the primitive function was taken. Through the differential reduction, the numerical solution of the angular flux density for the neutron transport equation was finally determined. In this work, numerical verifications were carried out for several examples of slab or spherical geometry. Critical systems as well as non-critical systems with different materials were simulated under the multi-group conditions. The calculation results show that the method proposed by this work has good accuracy, and in addition, the geometric and angular flux density has the novel characteristics of continuous distribution. The differential transform order theory and related techniques have been applied in the solving of the neutron transport equation and they are proved correct. Hence, a new technical way for the numerical solution of neutron transport equation has been explored in this work.