The irradiation swelling caused by fission gas can promote UO₂ fuel-cladding contact and reduce fuel thermal conductivity, which is a key behavior affecting fuel element performance. A fission gas irradiation swelling model for different burn-up ranges was established based on rate theory. The model first proposed control equations for intragranular gas, intergranular gas, and point defects under low burn-up. Then the control equations for intragranular gas considering grain subdivision and non-equilibrium growth of grain boundary pores under high burn-up were given. Finally, a model for coalescence and coarsening of grain boundary pores was established. On this basis, COMSOL software was used to solve the control equations. The model was preliminarily validated by experimental data. Results show that the predicted bubble size and porosity are in good agreement with the experimental results.