The structural integrity of nuclear fuel components under irradiation is critical to ensuring the safety and reliability of nuclear power plants. However, accurately simulating the mechanical behavior of these components using current constitutive models remains a formidable challenge. To this end, we propose a modified incremental constitutive model to approximate the irradiation creep and growth of nuclear fuel components. The proposed constitutive model effectively addresses the negative growth strain problem that existed in the past irradiation growth constitutive model. In order to study the irradiation characteristics of the proposed constitutive model, simple uniaxial tensile models are utilized. Subsequently, numerical simulations based on the modified irradiation constitutive model are performed to analyze the irradiation relaxation behavior of the leaf spring and irradiation-induced growth of the guide tube. The simulation results indicate that the developed model accurately captures the complex mechanical behavior under irradiation and is in excellent agreement with experimental data. This study on the irradiation constitutive model provides valuable insights into the mechanical behavior of nuclear reactor core components and contributes to the design and optimization of reactor components to enhance safety and performance.