This paper presents investigations on a usage of graphene as a voltage stabilizer for polyethylene blends in the potential recyclable high voltage direct current (HVDC) cable insulation. Thermal and electrical properties of the blends with/without graphene were evaluated by thermo-gravimetric analysis (TGA), differential scanning calorimetry (DSC), electrical treeing tests, DC conductivity and space charge measurements. Trap energy distributions in the blends were estimated using the measured space charge decay data. The obtained results show that additive-like amounts of graphene can improve the thermal stability of the polyethylene blends. The influence of the graphene on the tree inception voltage (TIV) of the polyethylene blends is not significant, whereas the low density polyethylene/high density polyethylene (LDPE/HDPE) with/without graphene demonstrates the highest TIV comparing to the LDPE, LDPE/polypropylene, and their corresponding graphene added materials. It is found that the DC conductivity of the polyethylene blends with/without graphene increases consistently with the increase of the temperature. The conductivity of the LDPE/HDPE decreases apparently with the inclusion of graphene. It has been shown that space charge accumulations can be suppressed by the addition of graphene in the polyethylene blends. It is postulated that the high trap level and trap energy density of the polyethylene blends with graphene are closely connected to the suppression of the space charge accumulation in the blends.