Sintering is a high temperature process used for ceramic or metallic powder consolidation that consists of concurrent densification and grain growth. This work presents a coupled solid-state sintering and grain growth model capable of studying large packings of particles within the Discrete Element Method (DEM) framework. The approach uses a refinement for large particle size ratios of previously established contact laws to model shrinkage. In addition, mass transfer between neighboring particles is implemented to model grain growth by surface diffusion and grain-boundary migration. The model assumptions are valid for initial and intermediate stage sintering. The model is validated on a two-particle system by comparing neck and particle size evolutions with those obtained by phase-field and meshedbased methods. Simulations on large packings (up to 400 000 particles) with particle size distributions originating from experiments are performed. The results of these simulations using physical data from the literature are compared to experimental data with good accordance of the key features of the microstructure evolution (densification kinetics, grain size-density trajectory, evolution of the mean grain size and of the size distribution). The simulations show that even at an early stage of sintering, hardly detectable grain growth actually affects the sintering kinetics to a non-negligible extent and that the realism of DEM simulations of sintering is improved when grain growth is considered. Taking advantage of the possibility to simulate large packings, the model elucidates the influence of the initial particle size distribution on the grain growth kinetics.