In this study, the impact of surface charge mobility on alternating current electroosmotic flow (ACEOF) in graphene nanochannels is the primary investigation. By taking into account the lateral movement of the adsorbed surface charge, the slip velocity condition of the hydrophobic surface is modified, and the impact of the adsorbed lateral movement surface charge on the volume flow is evaluated. In this work, the numerical method is employed to deal with the question, and an analytical solution at low potential is also provided. A number of important conclusions are drawn from the results of this study. For example, for incompressible Newtonian fluids, the increase in slip length will promote the oscillation amplitude of ACEOF. However, when the surface charge mobility is considered, the effect of slip length on it will be significantly reduced, and the volume flow will be further suppressed. In general, as the Reynolds number, bare slip length, and solution concentration increase, while the channel height and the absolute value of the surface charge density decrease, the inhibiting effect of surface charge mobility on the amplitude of the volume flow gradually intensifies. By adjusting the range of the above variables, the minimum inhibitory effect of surface charge mobility on volume flow amplitude can reach 0.65%, and the maximum inhibitory effect can reach 61.84%. These findings are of great practical importance for the design of efficient thermal nanodevices.