Fracture structures are important natural gas transport spaces in shale gas reservoirs, and their storage state in shale gas reservoirs seriously affects gas production and extraction efficiency. This work uses numerical modeling techniques to investigate the logging response law of the thermal and epithermal neutrons in the gas-containing fracture environment at various angles, applying neutron logging as a technical method. To increase the precision of the evaluation of the natural gas storage condition in shale gas reservoirs, the angle of the fractures’ neutron logging data is analyzed. It is found that even in an environment with the same porosity of the fractures, there are significant differences in the logging results due to the different angles of the fracture alignment: 1. the neutron counts in the high-angle (70–90°) fracture environment are 2.25 times higher than in the low-angle (0–20°), but the diffusion area of the neutrons is only 10.58% of that in the low-angle (0–20°); 2. in the neutron energy spectrum, neutron counts are spreading to the high-energy region (7–13 MeV) along with the increase in the angle of the fracture, and the feature is especially prominent in the approximately vertical (60–90°) fracture environment, which is an increase of 528.12% in comparison with the counts in the approximately horizontal angle (0–30°) environment. The main reason for these differences is the variation in the volume of the fracture within the source radiation. This volumetric difference results from the variation in fracture angles (even though the fracture porosity is the same). In view of the above phenomenon, this paper proposes the concept of “effective fracture volume”, which can intuitively reflect the degree of influence of fracture angle on neutron logging results. Further, based on the unique characteristics of shale gas reservoirs and neutrons, this paper provides important theoretical support for the modification of the porosity of the field operation, the evaluation of the physical characteristics of the gas endowment space, and the assessment.