Atoms in crystals will generate thermal diffuse scattering during thermal vibration. Thermal diffuse scattering analysis has great potential applications in condensed matter physics and material science research. Scandium oxide (Sc₂O₃) has unique physical and chemical properties, which make it have high research and application value. In this work, X-ray diffraction experiment is performed on Sc₂O₃ at room temperature of 26 ℃. The thermal diffuse scattering intensity exhibits a clear vibrational shape. The full diffraction back-based intensity equation of Sc₂O₃ is expanded, and the theoretical value of the thermal diffuse scattering intensity is calculated until the full diffraction back-based intensity spectrum of the 14th nearest atom (r = 0.3816 nm) is calculated. By fitting the theoretical value to the experimental value, we can see the inter-atomic thermal vibration correlation effect μ values corresponding to the nearest neighbor atom to the 7th nearest neighbor atom, the values of distance r from the nearest neighbor atom to the 7th nearest neighbor atom are 0.2067, 0.2148, 0.2161, 0.2671, 0.2945, 0.3229 and 0.3265nm, respectively, corresponding to their inter-atomic thermal vibration correlation effect μ values of 0.64, 0.63, 0.62, 0.61, 0.60, 0.58 and 0.57. Research result shows that the intensity of thermal diffuse scattering in Sc₂O₃ is closely related to the atomic thermal vibration, the most significant influence on the vibration shape of thermal diffuse scattering intensity is the thermal vibration correlation effect between the 7th nearest atom Sc₁-Sc₂. Inter-atomic thermal vibration correlation effect μ values will provide important parameters for studying the mechanical and thermal properties of materials, laying the foundation for the next-step calculating specific heat and interatomic force constant, and thus playing a crucial role in the use and development of materials.