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This paper proposes a coupling method involving the finite element (FE) equation of a discretized region and an analytical equation along with the field singularity of line currents in two-dimensional space. The singular field in the interior region is represented by Green's function of the line source, and the exterior region of air, conductor, or ferromagnetic material is represented by using the finite element method (FEM). An analytical expression for a magnetic field that contains unknown coefficients is coupled with the FE formulation for a coupled system equation with a matrix form. A numerical experiment relating to a line current near a ferromagnetic material shows the validity of this coupling method.