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The evaluation of current and magnetic field distributions in a railgun system during the launch is helpful to its structure design and efficiency improvement. In this paper, the finite-difference method (FDM) for the transient electromagnetic analysis of a railgun is presented. Using a 2-D analysis, the Peaceman-Rachford format is employed to the FDM to calculate current and flux density distributions. For the convenience of numerical experiment, a rectangle is used as the cross-sectional shape in railgun system at present. Also, as the prerequisite to calculate the current and the magnetic flux density distributions, the inductance gradient of rails is analyzed based on the phase method. The results of the simulation show how the distributions of both current density and magnetic field change during the discharge process.