The dependence of a numerically-simulated 'Del City' supercell storm on grid size is studied. A reference run with the grid size of 0.5 km successfully reproduces the supercell as demonstrated in the previous studies. In this sensitivity study, the grid size is varied from 1.0 km to 3.0 km with an interval of 100 m. When the grid size is less than 2.5 km, the storm evolves in a manner qualitatively similar to the reference run. When it is larger than 2.5 km, however, the evolution of the storm changes drastically because of an insufficient estimation of the shear-induced dynamic pressure. The present critical grid size is much smaller than that expected from the former sensitivity studies. Thus, one has to be more careful in choosing the grid size when performing a prediction of mesoscale convective systems, the behavior of which depends strongly on the behavior of individual meso-γ-scale convective storms.