In this study, the damage of a type of marble under uniaxial compressive loading was investigated using grain-based finite element simulations and a damage constitutive model. Accordingly, 40 Voronoi networks with different structural configurations and low and high joint densities were generated using the Phase2 software. Then, based on the calibrated parameters, uniaxial compression tests were numerically simulated on the generated networks. Finally, by utilizing the stress-strain curves derived from the numerical simulations and extracting the initial and damage moduli, the damage variable values were calculated as a function of strain. The results indicated that with an increase in the Voronoi joint density of the networks, the average values of both the initial and damage moduli decreased. Next, it was observed that with increasing strain up to a certain threshold, the damage variable increased gradually with a gentle slope. However, after reaching a critical strain value, the damage variable increased sharply with a very steep slope. This point, at which the damage begins to increase suddenly and rapidly, represents the onset of significant damage experienced by the rock specimen under uniaxial compressive conditions. Moreover, analysis of the failure patterns showed that tensile failures in networks with high Voronoi density occurred more frequently than in those with low density. Therefore, it can be concluded that the internal grain-based structure of rocks plays a crucial role in determining the extent of internal damage, failure patterns, and the dominant failure modes of rocks under uniaxial compressive loading conditions.