In this work, a discontinuous airfoil fin printed circuit heat exchanger (PCHE) was used as a recuperator in a micro gas turbine system. The effects of the airfoil fin geometry parameters (arc height, maximum arc height position, and airfoil thickness) and the airfoil fin arrangements (horizontal and vertical spacings) on the PCHE channel’s thermo-hydraulic performance were extensively examined by a numerical parametric study. The flow features, local heat transfer coefficient, and wall shear stress were examined in detail to obtain an enhanced heat transfer mechanism for a better PCHE design. The results show that the heat transfer and flow resistance were mainly increased at the airfoil leading edge owing to a flow jet, whereas the airfoil trailing edge had little effect on the thermo-hydraulic performance. The airfoil thickness was the most significant while the arc height and the vertical spacing were moderately significant to the performance. Moreover, only the airfoil thickness had a significant effect on the PCHE compactness. Based on a comprehensive investigation, two solutions NACA-6230 and -3220 were selected owing to their better thermal performance and smaller pressure drop, respectively, with horizontal spacings of 2 mm and vertical spacings of 2 or 3 mm.