Abstract: Oscillating impulse withstanding voltage test on GIS can help to find the internal defects of GIS. As to the common high voltage guide-bar protrusion defect, the breakdown voltage is usually lower under positive oscillating impulse voltage, but the corresponding breakdown process is still not clear. So this paper established a breakdown process mathematical model of SF₆ insulation gap under positive oscillating impulse voltage, performing numerical calculations of SF₆ insulation gap’s discharge process, based on the breakdown physical process of SF₆ gas. Through the effective electron generation, streamer inception and leader propagation the discharge process of the gap was quantitatively described, influence of space charge was considered and the characteristics of stepped leader was revealed. By conducting experiments on entity GIS, the accuracy of the model was verified. The model established in this paper can be used for the mathematical description of SF₆ insulation gap’s breakdown process under positive oscillating impulse voltage, and the breakdown characteristics can be calculated quantitatively.