Abstract: In analyzing the power density distribution within the core of a nuclear reactor, it is necessary to employ numerical methods to solve the neutron transport equation and obtain the neutron flux density distribution. Deterministic method, either the two-step or the one-step scheme, employed multi-group approximation techniques, which inevitably required the production of a special multi-group database and intricate resonance calculations. Although the probabilistic method could be calculated based on the continuous energy library, the computational efficiency could not meet the needs of large-scale engineering calculations. According to the characteristics of the microscopic cross-section data of the reaction between neutrons and nuclide nuclei under different energy conditions, the all-energy range was divided into resonance energy range and non-resonance energy range. In order to eliminate the multi-group approximation in the deterministic method, a method for calculating neutron transport equation in the non-resonant energy region based on function expansion was proposed. Initially, the non-resonant energy region was subdivided into segments, and within each segment, orthogonal polynomials serve as base functions for expanding the neutron flux density, which realized the processing of single energy independent variable in the neutron flight and absorption process, as well as the handling of double energy independent variable in the neutron scattering process. On the one hand, thermal neutrons were affected by the target nuclear thermal motion, chemical bond binding and scattering wave interference effect, leading to the phenomenon of up-scattering. On the other hand, fast neutrons were affected by a variety of different scattering reactions, resulting in down-scattering. Ultimately forming the coupling calculations between different energy ranges. Based on this foundation, the coupling calculation method between different energy segments in the non-resonant energy range was investigated, and an effective iterative calculation and numerical solution method was established. The solution for the neutron flux density distribution was transformed into solving the corresponding expansion coefficient moments, and then provided the distribution of neutron flux density and nuclear reaction rates within each energy segment. Finally, the neutron transport calculation program of continuous energy determination theory in non-resonant energy range was developed, and the different non-resonant nuclides were preliminarily verified, including single nuclide and multi-nuclide media. The computed results were compared with the existing continuous energy probabilistic neutron transport calculation program NECP-MCX. The verification results show that the relative deviation between the calculated values and the reference values is within 3.5%, demonstrating the feasibility of the continuous energy deterministic neutron transport calculation method based on function expansion.