Abstract: Dielectric functionally graded insulation can effectively improve the surface electric field distribution of an insulator and increase its surface flashover voltage without changing the geometrical structure of the insulator. At present, the design, fabrication and application of dielectric functionally graded insulators (d-FGIs) have become a hot issue in the field of electrical insulation, and two different types of d-FGI (i.e. bulk graded and surface graded insulators) have been proposed. In order to comprehensively compare them, the permittivity distribution of bulk and surface graded insulators are optimized based on the iterative algorithm of finite element method. The optimization results show that, in comparison with non-optimized uniform insulator, both the maximal electric field stress along the surface of bulk and surface graded insulators can be reduced by more than 70%. By investigating the influential factors such as the upper and lower limits of permittivity and the number of layers, the optimization effects of bulk and surface graded insulators are comparatively studied. Numerical simulation results show that the thickness of the surface layer of surface graded insulator is the key factor determining the difference in optimization effect between the bulk and the surface graded insulators.