Generally, space charge formation in dielectrics subjected to DC voltage results in the enhancement of a conduction current called space-charge-limited current (SCLC). In this study, we find an interesting phenomenon that the conduction current for a low-density polyethylene (LDPE) sheet does not increase with increasing applied voltage even though a large number of space charges are accumulated in its bulk. Simultaneous measurements of the conduction current and space charge distribution are carried out for a 150-μm-thick additive-free LDPE between a semiconduction anode and an aluminum-evaporated cathode. Under a low applied field of below 0.6 MV/cm, the current is proportional to the square of the applied field because the maximum field strength in LDPE becomes higher than the mean applied field strength due to space charge formation in the LDPE bulk. Both the space charge distributions and the corresponding field distributions obtained by the simultaneous measurement roughly agree with the theoretical distributions based on the SCLC model. By increasing the applied field, however, the steady-state current saturates although a large number of positive space charges are accumulated in the LDPE bulk. We confirm that the steady-state current is restricted when a large number of frozen positive charges in front of the cathode are formed causing the strong field enhancement at a limited local thin area. These results imply that the carrier mobility at the local thin area was reduced by the excess field enhancement.