This study presents a four-terminal (4T) perovskite-chalcogenide tandem solar cell (TSC) that includes quasi-2D perovskite material in the top sub-cell in order to provide a stable structure, and the bottom sub-cell contains Zn(O,S,OH) material to provide a nontoxic buffer layer. First, a reference TSC with a total power conversion efficiency (PCE) of 26.48% is modeled, using MAPbI3 and CIGSSe as 3D perovskite and chalcogenide absorber layers (ALs), respectively. Next, two structures are designed to produce a stable SC using the Ruddlesden Popper (RP) quasi-2D perovskite materials, which have the chemical formula BA2MAm−1PbmI3m+1, m = 2–5. The initial structure uses quasi-2D perovskites in place of the 3D perovskite AL. According to the results, BA2MAPb2I7 represents the maximum PCE of 16.00%, 10.48% less than previously. This is caused by quasi-2D materials’ high Eg and low carrier mobility. In the second structure, 3D perovskite AL is capped with the quasi-2D perovskites. In terms of attaining maximum PCE, the optimal TSC is found for BA2MA3Pb4I13 with a PCE of 25.80%. Compared to the initial structure, this one’s PCE increased by 61.25%. In order to boost PCE, a 80 nm-thick anti-reflection (AR) layer is added to the second structure, and the PCE increased to 27.48%. Therefore, the final TSC is proposed as a 4T quasi-2D/3D perovskite-chalcogenide TSC that is stable, and has nontoxic buffer layer, with 3.78% more PCE than the reference structure.