β-Ga₂O₃ has a large band gap of 4.7~4.9 eV and a high critical electric field strength of 8 MV/cm. These properties allow β-Ga₂O₃ devices to operate at high power and strong radiation. In nuclear radiation environments, β-Ga₂O₃ devices will face significant challenges. The β-Ga₂O₃ material can generate many point defects in high-energy particle irradiation. The existence of strain field around the point defects, clusters with lower strain energy can be formed through migration and aggregation, and defects with more serious damage can be formed. However, the mechanism of irradiation defect migration in β-Ga₂O₃ materials has not been reported.The first principles calculation in this paper is based on density function theory, and the Perdew Burke Ernzerhof (PBE) functional under Generalized Gradient Approximation (GGA) is used to describe the exchange-correlation interaction of electrons. Considering that PBE method often underestimates the bandgap calculation, a hybrid functional HSE06 is used to introduce some Hartree-Fock interchange terms into the traditional GGA functional, which effectively improves the accuracy of bandgap calculation. The migration barrier of defects is calculated by the Climbing-Image Nudged Elastic Band (CI-NEB) method, which can accurately find the minimum energy path between the initial state and the final state and the corresponding transition state, which is helpful to further understand the migration behavior of defects.The results show that compared with Ga atoms, O atoms are more easily detached from lattice position to form V_O and O_i. For V_O defects, the migration barrier shows point-to-point dependence, and 23 possible migration paths are studied. The migration barrier of V_O1 is the smallest in the 3 direction (migration barrier is_{0.48 eV). This low barrier indicates that VO1 can migrate spontaneously along this path at normal temperature. VO2 has the lowest migration barrier in the 11 direction (migration barrier is 0.015 eV) and almost no migration barrier, which means that VO2 has a very high migration activity at room temperature, which may significantly affect the electrical and optical properties of the material. The optimal migration path of VO3 is located in the direction of 18, and the corresponding migration barrier is 0.39 eV, which also has the possibility of migration at room temperature. In contrast, the migration barrier of VGa is relatively high, but there is still a relatively easy migration path: the optimal migration path of VGa1 is located in the 4 direction, and its migration barrier is 0.33 eV, which is slightly higher than the barrier of partial oxygen vacancy, but it is still possible to migrate under external excitation (such as irradiation, temperature increase, or electric field). VGa2 is also the easiest to migrate in the 4 directions with a corresponding barrier of 0.35 eV, indicating that its migration characteristics are similar to VGa1. The migration barrier of VO is generally lower than that of VGa, indicating that VO is more active in β-Ga2O3 crystals. Under irradiation or high temperature environment, the migration of VO may cause significant changes in material properties. According to the analysis of Oi migration path, the migration barrier corresponding to Oi2→Oi path is low (0.13 eV), which is significantly lower than the energy barrier of other Oi paths. It is shown that the Oi atoms are more inclined to migrate along this path in the crystal. In addition, due to the lower migration barrier, Oi2 path defects are more likely to accumulate or migrate under external excitation (such as irradiation). For Gai atom migration, Gai1→Gai6 is the optimal migration path, and the corresponding migration barrier is only 0.84 eV, which is much lower than other Gai migration paths. This low barrier value means that under certain conditions, Gai atoms have strong mobility, especially in the irradiation environment, and its dynamic behavior may have profound effects on the conductivity and stability of materials. The research results will help to further understand the microscopic mechanism of defect migration in β-Ga2O3 materials under irradiation and provide theoretical reference for irradiation reinforcement.}