As an important component of the system, the performance of the printed circuit heat exchanger (PCHE) has a significant impact on the efficiency and compactness of the supercritical carbon dioxide (SCO2) Brayton cycle system. Optimization of the structural parameters of airfoil fins can improve the performance of PCHE flow channels, but it has not received enough attention. Therefore, it is of great significance to investigate the effects of structural parameters such as the maximum thickness (Wf), the distance from the position where the maximum thickness is located to the leading-edge (Df), and the radius of the leading-edge (Rf) of the airfoil fins on the flow heat transfer performance of SCO2 in the channel of PCHE. A three-dimensional numerical model is developed and validated for performance analysis of the PCHE, meanwhile the thermal-hydraulic performance of channels with different structural parameters of the airfoil fins is compared. The results show that with the increase of the Wf of the airfoil fins, the heat transfer characteristics of the PCHE channel are gradually enhanced, and the flow characteristics are gradually weakened. When the maximum thickness of the airfoil fins is in the front, the heat transfer and flow characteristics of the PCHE channel are better. As the Rf of the airfoil fins increases, the heat transfer characteristics and flow characteristics of the PCHE channel fluctuate. The change of the turbulent kinetic energy, the boundary layer thickness, the synergistic effect of the velocity field and the temperature gradient field, and the local entropy production in the channel can well explain the mechanism of the flow and heat transfer of the SCO2 in the airfoil fin channel. In addition, among the channels with different structural parameters of the airfoil fins, the Fin-5 airfoil fin channel with Wf of 1.5 mm, the Fin-6 airfoil fin channel with Df of 0.6 mm and the Fin-13 airfoil fin channel with Rf of 1.46 mm are recommended. Their comprehensive performance is 2.0–6.3%, 0.9–5.6% and 0.13–1.81% higher than that of the Fin-3 airfoil fin channel, respectively.