The impulse breakdown attributes are of rudimentary importance in the insulation coordination in the gas-insulated switchgear (GIS). The critical voltage waveshape for the insulation is the surge over voltages. Usually, such over-voltages will emerge on the electrical equipment while these are burdened under DC or AC working voltages. Therefore, during relatively small-time intervals, the undermined devices are exposed to surge voltages that are superimposed upon the already running DC or AC voltages. From a safety point of view, and for providing reliable power to the consumer, we need to study the breakdown characteristics under such over-voltages, with reference to normal operating voltages (DC or AC). The breakdown mechanism of the GIS under compressed SF6 gas is known to be controlled by a stepped leader propagation method. Although different experimental studies have been conducted by many researchers for different experimental conditions under DC, AC, or impulse high voltages alone, not much research has been performed, in a systematic way, to model and estimate the breakdown voltages of the GIS under such superimposed conditions. This paper presents a systematic model, using a leader propagation technique for the estimation of breakdown voltages for complex voltage conditions, i.e., a lightning impulse (LI) superimposed on pre-stressed DC for different experimental conditions. The estimated values are in good agreement with the measured experimental results.