To calculate the distribution of the magnetic field and eddy current density on the surface of an aluminium plate, a method that couples the face-smoothed finite element method (FS-FEM) to the boundary element method (BEM) is proposed in this study. This method combines the advantages of the FS-FEM and BEM, which can rapidly and accurately calculate the distributions of vertical magnetic field and eddy current field on the surface of an aluminium plate. The structural parameters and material properties of the coil and aluminium plate are considered. An accurate three-dimensional calculation model is established. Then, the vertical magnetic field and eddy current field distributions are calculated in this study. In the case of the same grid density, compared with the finite element–boundary element coupling algorithm, the simulation results show that the FS-FEM and the boundary element coupling method have obvious advantage in improving the calculation accuracy. The maximum relative error between the calculated results and measured results is only 4%. The proposed method in this study is available for reference to the transient open-domain eddy current field analysis.