Recent experiments suggest graphene-based materials as candidates for use in future electronic and optoelectronic devices. In this study, we propose a new multilayer quantum dot (QD) superlattice (SL) structure with graphene as the core and silicon (Si) as the shell of QD. The Slater–Koster tight-binding method based on Bloch theory is exploited to investigate the band structure and energy states of the graphene/Si QD. Results reveal that the graphene/Si QD is a type-I QD and the ground state is 0.6 eV above the valance band. The results also suggest that the graphene/Si QD can be potentially used to create a sub-bandgap in all Si-based intermediate-band solar cells (IBSC). The energy level hybridization in a SL of graphene/Si QDs is investigated and it is observed that the mini-band formation is under the influence of inter-dot spacing among QDs. To evaluate the impact of the graphene/Si QD SL on the performance of Si-based solar cells, we design an IBSC based on the graphene/Si QD (QDIBSC) and calculate its short-circuit current density (Jsc) and carrier generation rate (G) using the 2D finite difference time domain (FDTD) method. In comparison with the standard Si-based solar cell which records Jsc = 16.9067 mA/cm2 and G = 1.48943 × 1028 m-3-s-1, the graphene/Si QD IBSC with 2 layers of QDs presents Jsc = 36.4193 mA/cm2 and G = 7.94192 × 1028 m-3-s-1, offering considerable improvement. Finally, the effects of the number of QD layers (L) and the height of QD (H) on the performance of the graphene/Si QD IBSC are discussed.