In this paper, the total dose effect of graphene field-effect transistors (GFET) of different structures and sizes was studied. The irradiation experiments were carried by 10-keV X-ray irradiation platform with a dose rate of 200 rad(Si)/s. Positive gate bias (<i>V<sub>G</sub></i>=+1 V, <i>V<sub>D</sub></i>=<i>V<sub>S</sub></i>=0 V) was applied during irradiation. Using a semiconductor parameter analyzer, the transfer characteristic curves of top-gate and back-gate GFETs were obtained both before and after irradiation. At the same time, the degradation condition of the Dirac voltage <i>V<sub>Dirac</sub></i> and the carrier mobility <i>μ</i> are extracted from the transfer characteristic curve. The experimental results demonstrate that <i>V<sub>Dirac</sub></i> and carrier mobility <i>μ</i> degrade with increasing dose. the depletion of <i>V<sub>Dirac</sub></i> and carrier mobility <i>μ</i> is caused by the oxide trap charge generated in the gate oxygen layer during X-ray irradiation. Compared with the back-gate GFETs, the top-gate GFETs show more severe degradation of <i>V<sub>Dirac</sub></i> and the carrier mobility, therefore Top-gate GFETs are more sensitive to X-ray radiation at the same cumulative dose than back-gate GFETs. The analysis found that, the degradation of top-gate GFET is mainly caused by the oxide trap charge. And in contrast to top-gate GFET, oxygen adsorption contributes to the irradiation process of back-gate GFET, which somewhat mitigates the impacts of radiation damage. Furthermore, a comparison was made between the electrical property deterioration of GFETs of varying sizes between the pre-irradiation and post-irradiation. The back-gate GFET, which had the size of 50 μm*50 μm, and the top-gate GFET, which had the size of 200 μm*200 μm were found to have sustained the most damage. In the case of the top-gate GFET, the larger the radiation area, the more oxide trap charges generated, the more serious the damage. In contrast, back-gate GFETs have a larger oxygen adsorption area during irradiation and a more noticeable oxygen adsorption effect, which partially offsets the damage produced by irradiation. Lastly, the oxide trap charge mechanism was simulated using TCAD simulation tool. TCAD simulation reveals that the trap charge at the interface of Al<sub>2</sub>O<sub>3</sub> and graphene is the primary cause of top-gate GFET property degradation. It has a significant impact on the the investigation of the radiation effect and radiation reinforcement of GFETs.