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High voltage electrical pulse (HVEP) is an innovative technique with the low-energy and high efficiency. However, the underlying physics of the electric breakdown within the rock, and the coupling mechanism between the various physical fields involved in HVEP still need to be further understood. In this study, we establish a two-dimensional numerical model of multi-physical field coupling the electrical breakdown of porous rock with randomly distributed pores to investigate the effect of pore characteristics (porosity, pore media composition) on the partial electrical breakdown of rock (i.e. the generation of plasma channel inside the rock). The findings indicate that the generation of a plasma channel is directionally selective and extends in the direction of a weak electrical breakdown intensity. As the porosity of rock increases, so does the intensity of the electric field in the "electrical damage" region—the greater the porosity, the greater the effectiveness of rock breaking. In addition, as the fraction of pore fluid (Swater/Sair) declines gradually, the generation time of the plasma channel lowers, and the efficacy of rock-breaking by HVEP increases. In addition, this article conducted an indoor experiment utilizing an electric pulse drill to break down the rock to recreate the growth mode of the plasma channel in the rock. Moreover, the experimental results are consistent with the simulation results; additionally, the development type of partial electric breakdown is verified to be related to electrode polarity and pore characteristics via the experiment of the symmetrical needle-needle electrode arrangement, which further demonstrates the mechanism of partial electric breakdown. This research is significant for comprehending the process of electric impulse rock-breaking and gives theoretical guidance and technological support for advancing electric impulse drilling technology.