The space charge accumulation properties under dc high stress at various temperatures were investigated in cross-linked polyethylene (XLPE) and XLPE/Carbon composite. We have reported, earlier, that low density polyethylene (LDPE) including inorganic nano-size filler shows a good performance without accumulation of space charge even under very high dc electric field. Since it can be thought that the nano-size filler with the higher permittivity shows the superior effect of suppression of the charge injection from electrodes into the bulk of sample under dc high stress, we tried to use the conductive nano-size filler which has the infinite permittivity ideally. In this report, we have tried to investigate the space charge accumulation properties of XLPE with and without graphene nano-filler.