While the available finite-difference time-domain (FDTD) subgridding schemes can improve the solution accuracy over those of the traditional FDTD, it is known to have instability problems. A new subgridding scheme combining FDTD or FDTD(2,4) method with FD-Laplacian interpolation is proposed. By applying subgridding scheme at fine components in a structure, the necessary field resolution can be obtained. In this scheme, FD-Laplacian interpolation is applied in the coarse main grids only or both the coarse main grids and the subgrids, and the error introduced and the floating point operations required can be reduced significantly. The accuracy of the scheme is tested by computing the resonant frequencies of two cavities and solving a scattering problem. The results are compared with solutions for uniformly mesh FDTD method and other FDTD subgridding schemes. The proposed method is stable after 100 000 time steps.