A general method for solving the differential equations of electric field lines based on numerical computation is proposed. The singularity issues in the solving process are discussed, and the procedure for solving the differential equations is simplified. Using Igor Pro, numerical solutions and visualizations are performed for the electric field line equations of an isolated point charge, a pair of like charges, a pair of opposite charges, a pair of like long straight wires, a pair of opposite long straight wires, and complex electric fields. The accuracy of the point-by-point solution based on the Taylor expansion grid method is compared with that of the numerical differential equation solution.