In the fusion power conversion system, a printed circuit heat exchanger (PCHE) between molten salt (MS) and supercritical carbon dioxide (sCO2) transfers huge heat between loops. To improve heat transfer efficiency, a new heterogeneous PCHE with MS zigzag passage and sCO2 airfoil fin passage was proposed. A one-dimensional simulation of the new PCHE was conducted to study the effects of the plate number and the length on its pressure drop, MS mass flowrate, capital cost, and operating cost. Then, a new single objective optimization of the total cost was performed by the genetic algorithm (GA) based on the Chinese Fusion Engineering Testing Reactor (CFETR) parameters. Finally, the new optimal PCHE was compared with the PCHE with MS straight passage and sCO2 airfoil fin passage. The results show that the length and the plate number of the PCHE have an important effect on the pressure drop and its cost. The optimal geometry scheme with the minimum cost is given for the application to CFETR. By comparison with the MS straight-passage PCHE, it is found that the total cost of the new PCHE is reduced by 5.7% and the volume of the heat exchanger is reduced by 10.7%.