High-voltage pulse discharge (HVPD) in liquid technology, when applied to the demolition of concrete structures, has the advantages of green environmental protection, saving energy, emission reduction, safety, reliability, etc. However, research on the influence law of various factors on the effect of crushing is still insufficient. Therefore, this manuscript equated the shock load caused by HVPD to the blasting load and introduced a cohesive zone model based on ABAQUS. The whole process of a concrete column being subjected to a shock wave generated by pulse power discharge was simulated and analyzed. To validate the model’s reasonableness, a comparison and analysis were conducted with the results of experimental studies on concrete column fractures caused by HVPD in liquid. The study further investigated the influence of three parameters—one-side longitudinal reinforcement ratio, volume hoop ratio, and concrete grade strength—on the degree of fracture of the concrete column with a single row of holes (i.e., the width of transverse cracks or longitudinal cracks around the drilled holes). The simulation results revealed that the width of transverse cracks decreases significantly with the increase in the one-side longitudinal reinforcement ratio of the column, while the width of longitudinal cracks decreases substantially with the increase in the volume hoop ratio of the column. In addition, the degree of fracture of concrete columns decreases slightly with the increase in the concrete grade strength. Based on the simulation results, the mathematical expressions between the crack widths (transverse crack width and longitudinal crack width) and the key parameters, such as the one-side longitudinal reinforcement ratio of the column, volume hoop ratio of the column, and concrete grade strength, were established, respectively. These expressions facilitate their practical application in engineering practice.