Start-up is one of the critical phases for tokamak discharge. The electron drift injection (EDI) system has been developed on J-TEXT for start-up studies. A breakdown experiment with EDI-assisted start-up has been conducted, which verified the effect of pre-ionization by EDI to achieve start-up at a lower ohmic field voltage. A zero-dimensional (0D) model has been developed to explain the effect of EDI quantitatively. The comparison between the experiment and simulation verified the credibility of this model. Based on this model, a comparison between pure ohmic heating start-up and EDI-assisted start-up was presented, showing that EDI improved ionization, causing a lower delay to the peak of hydrogen ionization and radiation losses and a smoother rise in the electron and ion energy. This result quantitatively verified the pre-ionization effect of EDI on start-up . The effects of injecting different currents and electron energy were investigated. A better pre-ionization effect was realized by increasing the injected current, which can be a reference for the upgrading of the EDI system.