A vacuum Interrupter (VI), a core part that composes the breaking part of medium-voltage vacuum circuit breaker (VCB), has the excellent insulation performance and arc-extinguishing capability. SF6 gas had been used for the external insulation of VIs since the dielectric strength of SF6 gas is superior to that of other insulation gases. However, because of environmental problems related with global warming, a solid-insulated technology was recently researched. The functionally graded material (FGM), as changing spatially the distribution of the relative permittivity inside an insulator, can reduce the electric field stress at the specific region. Especially, the external insulation performance of the VI with the molded FGM insulator is greatly improved as compared with that of the existing VI or the VI with a new external shield. In this paper, the effectiveness of this FGM insulator is verified by the numerical simulation.