EEG source imaging is able to reconstruct sources in the brain from scalp measurements with high temporal resolution. Due to the limited number of sensors, it is very challenging to locate the source accurately with high spatial resolution. Recently, several total variation (TV) based methods have been proposed to explore sparsity of the source spatial gradients, which is based on the assumption that the source is constant at each subregion. However, since the sources have more complex structures in practice, these methods have difficulty in recovering the current density variation and locating source peaks. To overcome this limitation, we propose a graph Fractional-Order Total Variation (gFOTV) based method, which provides the freedom to choose the smoothness order by imposing sparsity of the spatial fractional derivatives so that it locates source peaks accurately. The performance of gFOTV and various state-of-the-art methods is compared using a large amount of simulations and evaluated with several quantitative criteria. The results demonstrate the superior performance of gFOTV not only in spatial resolution but also in localization accuracy and total reconstruction accuracy.