The dual-cooled annular nuclear fuel is an advanced design that is expected to greatly lower fuel temperature even under high linear power density, as compared to traditional cylindrical fuel pin. Although fuel temperature can be much lower, the annular pellet also receives much higher neutron fluence, which may induce severe cracking during normal operation. This work deals with quasi-static cracking of dual-cooled annular UO2 pellet under neutron radiation. The analysis is based on the phase-field fracture model coupled with an oxygen diffusion model, heat conduction model and mechanical equilibrium model. The considered thermo-mechanical properties and irradiation behaviors of the nuclear fuel are both temperature and irradiation dependent. Especially, the acceleration of fuel creep due to oxygen redistribution is included. The fracture is represented by a scalar phase-field variable governed by a cohesive phase-field fracture method. These models are numerically implemented in the multi-physics coupling simulation framework MOOSE. For the first time, the diffusion-thermo-mechanical coupled fracture model is applied to the dual-cooled annular UO2 fuel pellet cracking during reactor startup, power ramp and reactor shutdown. Preliminarily, UO2 irradiation creep is found to play an important role on the fuel pellet fragmentation. The developed capability supports interpretation of experimental data and can guide material design of advanced ceramic nuclear fuel.