The transient conductivity in low-density polyethylene is studied. Isochronal current-voltage measurements for 1800 s and 1 day time intervals are carried out under dry NZ atmosphere. When after every measurement the sample is fully discharged at high temperature the isochronal current - voltage characteristic reveals an ohmic behavior. When the next field increase is applied without sample discharging the current-voltage characteristic is super-quadratic. We explain this increase of the current assuming that a fraction of the previous injected charge is detrapped by the field and it contributes to current increase. Consequently the current-voltage characteristic is strongly dependent on the time lag between two successive rises in the field. Neither the Poole-Frenkel mechanism nor the Richardson Schottky mechanism can by used to explain the experimental results. The isothermal charging and discharging currents are explained assuming the movement of injected/ejected charge in the resultant local field. The values obtained for the adjustable parameters of the model are in good agreement with the values in the literature.