In this study, the effect of heat sink geometries on the performance of a thermoelectric generator was researched. In this context, fins with different geometries (flat fin, square pin fin, hexagonal pin fin, and circle pin fin) placed on an aluminum heat sink, and their effects on heat transfer and electricity generation were investigated numerically. Calculations were carried out according to three different hot surface temperatures and five different air velocities. As a result of this study, it was determined that the electrical output increased with the increase in air velocity and hot surface temperature in all geometries. The highest electrical outputs were obtained at 150 °C hot surface temperatures and 15,000 Reynolds numbers, while the lowest electrical outputs were obtained at 50 °C hot surface temperatures and 5000 Reynolds numbers in all geometries. The best thermal and electrical performance was obtained with a flat fin heat sink, and the worst performance was seen in the thermoelectric generator (TEG) system without a heat sink. The highest power outputs of the flat fin heat sink and without heat sink TEG systems were 6.42 W and 1.12 W, respectively. In addition, the highest conversion efficiencies of the flat fin heat sink and without heat sink TEG systems were 14.94% and 5.54%, respectively.