In this paper, the total dose effects of graphene field-effect transistors (GFETs) with different structures and sizes are studied. The irradiation experiments are carried out by using the 10-keV X-ray irradiation platform with a dose rate of 200 rad(Si)/s. Positive gate bias (V_G = +1 V, V_D = V_S = 0 V) is used during irradiation. Using a semiconductor parameter analyzer, the transfer characteristic curves of top-gate GFET and back-gate GFET are obtained before and after irradiation. At the same time, the degradation condition of the dirac voltage V_Dirac and the carrier mobility μ are extracted from the transfer characteristic curve. The experimental results demonstrate that V_Dirac and carrier mobility μ degrade with dose increasing. The depletion of V_Dirac and carrier mobility μ are 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 severely degrade V_Dirac and carrier mobility, therefore top-gate GFET is more sensitive to X-ray radiation at the same cumulative dose than back-gate GFET. The analysis shows 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 effect of radiation damage. Furthermore, a comparison of electrical property deterioration of GFETs of varying sizes between the pre-irradiation and the post-irradiation is made. The back-gate GFET, which has a size of 50 μm×50 μm, and the top-gate GFET, which has a size of 200 μm×200 μm, are damaged most seriously. In the case of the top-gate GFET, the larger the radiation area, the more the generated oxide trap charges are and the more serious the damage. In contrast, the back-gate GFET has a larger oxygen adsorption area during irradiation and a more noticeable oxygen adsorption effect, which partially offsets the damage produced by irradiation. Finally, the oxide trap charge mechanism is simulated by using TCAD simulation tool. The TCAD simulation reveals that the trap charge at the interface between Al₂O₃ and graphene is mainly responsible for the degradation of top-gate GFET property, significantly affecting the investigation of the radiation effect and radiation reinforcement of GFETs.