In the realm of direct current (DC) resistivity exploration, traditional three-dimensional (3D) point-source forward calculations are often hindered by high computational complexity and substantial resource requirements. While Fourier transformation can reduce this complexity to a 2.5D model, it still does not match the efficiency of a two-dimensional (2D) line-source model. To address these challenges, we introduce an innovative algorithm for 2D line-source DC resistivity numerical simulation. Our approach leverages Fourier transformation to convert the 2D problem into a one-dimensional (1D) problem in the wavenumber domain, subsequently employing the finite difference method for resolution. We further incorporate the tight operator iterative technique to significantly enhance computational efficiency and convergence velocity. A suite of numerical experiments confirms that our algorithm not only maintains the accuracy of simulation results but also exhibits superior convergence characteristics. Additionally, by comparing the anomaly responses of point-source and line-source models in both high-resistivity and low-resistivity geophysical scenarios, we demonstrate the line-source model's heightened sensitivity to anomalies. This study not only equips the DC electrical exploration field with a efficient modeling tool but also contributes novel theoretical insights for the interpretation of geophysical data.