This paper presents a grid snapping technique, called multi-resolution fuzzy grid snapping (MFGS), that enables automatic mouse cursor snapping for a multi-resolution grid system. Quick and frequent switching between high- and low-resolution grid snapping is essential to make geometrical drawings that include both fine and coarse structures when using CAD systems with ordinary single-resolution grid systems. MFGS is intended to relieve users of this tedious manual switching. MFGS dynamically selects an appropriate snapping resolution level from a multi-resolution grid system according to the pointing behavior of the user. MFGS even supports an extremely fine grid resolution level, which is referred to as the no-snapping level. We show experimental results which demonstrate that MFGS is an effective grid snapping technique that speeds up low-resolution grid snapping while retaining the ability to snap to high-resolution grids. Furthermore, we examine the role of fuzziness in MFGS and its effect on snapping performance.