Among the most commonly used algorithms for tackling the linearized equations of continuum mechanics for acoustic scattering of target is the staggered second-order finite-difference time-domain (FDTD) schemes. These schemes offer simplicity, ease of implementation and the potential for parallelization, which is particularly relevant in the era of exascale computing. Unfortunately, their low resolution due to the formal low-order and stair-step representation of media interfaces (e.g. target/water) necessitates a fine grid resolution, resulting in significant computational costs in three-dimensional configurations. To overcome this issue, a FDTD multi-grid method is proposed. The mesh is refined locally near the interfaces, while a coarse grid is used in homogeneous regions. In the fine grids, the FDTD scheme is applied, and in the coarse grid, higher-order staggered schemes are used to counterbalance the reduction in resolution due to the larger spacing. High-order interpolation is used to match the solutions at the grid interfaces. The effectiveness of the technique will be tested on the scattering of buried objects.