A multilevel finite difference time domain (FDTD) subgridding scheme coupled with interpolation based on finite difference approximation to the Laplacian operator is presented. In order to model a structure with small components using FDTD method, the accuracy of the results can be improved by utilizing a new multilevel FDTD subgridding scheme. In this scheme, an FD-Laplacian interpolation is applied in both the coarse main grids and the subgrids to further reduce the error. The validation 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 traditional FDTD and other FDTD subgridding schemes published in the literature.