Predicting the electrical breakdown of polymers is critical for certifying the endurance and lifetime of high voltage power equipment. Since various factors contribute nonlinearly to the breakdown phenomena of polymer insulators, it is difficult to assess the impact of each factor independently. In this study, we numerically analyzed the breakdown phenomenon because of the ramp rate of the DC voltage applied to a polymer insulator, low-density polyethylene (LDPE), using the finite element method (FEM). To predict the breakdown initiation, we analyzed the relaxation time of the conduction current through the insulator as a significant indicator. The bipolar charge transport (BCT) model was used to analyze the charge behavior within the LDPE, and the breakdown voltage was predicted by incorporating the molecular displacement model. This analysis was conducted for a wide range of ramp rates from 10 to 1500 V/s. The current density was calculated using two different methods, namely the energy and average methods, and the results were compared with each other. The results of the numerical model were further verified by comparing with those from experiments reported in the literature.