The influx of a switching impulse during DC steady-state operations causes severe electrical stress on the insulation of HVDC cables. Thus, the insulation should be designed to withstand a superimposed switching impulse. All major manufacturers of DC cables perform superimposed switching impulse breakdown tests for prequalification. However, an experimental approach to study space charge dynamics in dielectrics under a switching impulse superposed on DC voltage has not been reported yet. This is because, unlike the DC stress, it is not possible to study the charge dynamics experimentally under complex stresses, such as switching impulse superposition. Hence, in order to predict and investigate the breakdown characteristics, it is necessary to obtain accurate electric field distribution considering space charge dynamics using a numerical approach. Therefore, in this paper, a numerical study on the switching impulse superposition was carried out. The space charge dynamics and its distribution within the dielectric under DC stress were compared with those under a superimposed switching impulse using a bipolar charge transport (BCT) model. In addition, we estimated the effect of a superimposed switching impulse on a DC electric field distribution. It was concluded that the temperature conditions of dielectrics have a significant influence on electric field and space charge dynamics.