Three-dimensional numerical models of potential underground storage and compositional simulation are a way to study the feasibility of storing carbon dioxide in the existing geological formations. However, the results of the simulations are affected by many numerical parameters, and we proved that the refinement of the model grid is one of them. In this study, the impact of grid discretization on CO2 trapping when the CO2 is injected into a deep saline aquifer was investigated. Initially, the well bottom-hole pressure profiles during the CO2 injection were simulated using four different grids. As expected, the results confirmed that the overpressure reached during injection is strongly affected by gridding, with coarse grids leading to non-representative values unless a suitable ramp-up CO2 injection strategy is adopted. Then, the same grids were used to simulate the storage behavior after CO2 injection so as to assess whether space discretization would also affect the simulation of the quantity of CO2 trapped by the different mechanisms. A comparison of the obtained results showed that there is also a significant impact of the model gridding on the simulated amount of CO2 permanently trapped in the aquifer by residual and solubility trapping, especially during the few hundred years following injection. Conversely, stratigraphic/hydrodynamic trapping, initially confining the CO2 underground due to an impermeable caprock, does not depend on gridding, whereas significant mineral trapping would typically occur over a geological timescale. The conclusions are that a fine discretization, which is acknowledged to be needed for a reliable description of the pressure evolution during injection, is also highly recommended to obtain representative results when simulating CO2 trapping in the subsurface. However, the expedients on CO2 injection allow one to perform reliable simulations even when coarse grids are adopted. Permanently trapped CO2 would not be correctly quantified with coarse grids, but a reliable assessment can be performed on a small, fine-grid model, with the results then extended to the large, coarse-grid model. The issue is particularly relevant because storage safety is strictly connected to CO2 permanent trapping over time.