Charging and discharge currents measured in low-density polyethylene (LDPE) and LDPE/Al2O3 nanocomposite are analyzed. The experiments were conducted at temperatures of 40–80 °C utilizing a consecutive charging–discharging procedure, with the charging step at electric fields varying between 20 and 60 kV/mm. A quasi-steady state of the charging currents was earlier observed for the nanofilled specimens and it was attributed to the enhanced trapping process at polymer–nanofiller interfaces. An anomalous behavior of the discharge currents was found at elevated temperatures for both the studied materials and its occurrence at lower temperatures in the nanofilled LDPE was due to the presence of deeply trapped charges at polymer–nanofiller interfaces. The field dependence of the quasi-steady charging currents is examined by testing for different conduction mechanisms. It is shown that the space-charge-limited process is dominant and the average trap site separation is estimated at less than 2 nm for the pristine LDPE and it is at about 5–7 nm for the LDPE/Al2O3 nanocomposite. Also, location of the trapping sites in the band gap structure of the nanofilled material is altered, which substantially weakens electrical transport as compared to the unfilled counterpart.