The role of trap characteristics in modulating charge transport properties is attracting much attentions in electrical and electronic engineering, which has an important effect on the electrical properties of dielectrics. This paper focuses on the electrical properties of Low-density Polyethylene (LDPE)/graphene nanocomposites (NCs), as well as the corresponding trap level characteristics. The dc conductivity, breakdown strength and space charge behaviors of NCs with the filler content of 0 wt%, 0.005 wt%, 0.01 wt%, 0.1 wt% and 0.5 wt% are studied, and their trap level distributions are characterized by isothermal discharge current (IDC) tests. The experimental results show that the 0.005 wt% LDPE/graphene NCs have a lower dc conductivity, a higher breakdown strength and a much smaller amount of space charge accumulation than the neat LDPE. It is indicated that the graphene addition with a filler content of 0.005 wt% introduces large quantities of deep carrier traps that reduce charge carrier mobility and result in the homocharge accumulation near the electrodes. The deep trap modulated charge carrier transport attributes to reduce the dc conductivity, suppress the injection of space charges into polymer bulks and enhance the breakdown strength, which is of great significance in improving electrical properties of polymer dielectrics.