Printed circuit heat exchangers (PCHEs) have been widely proposed to enhance energy conversion efficiency in the nuclear power-related system, e.g. in the supercritical CO2 Brayton cycle for advanced nuclear power systems. The thermal-hydraulic characteristics of PCHEs are greatly affected by the layouts of channels, which have drawn more attention. Currently, the channel types for PCHEs mainly involve traditional straight channels, zigzag channels, airfoil channels, etc. In this work, a novel bioinspired fractal-tree microchannel (FTMC) structure for PCHEs is proposed, optimized, and assessed. The non-dominated sorting genetic algorithms II (NSGA-II) improved by the elite-retained strategy is applied for the design of geometrical parameters (dimension ratio, bifurcation number, initial width and length) in fractal-tree PCHE (FT-PCHE) for trading off the total thermal resistance and pumping power. The optimal solutions (Pareto front) are obtained. The thermal-hydraulic performance of FT-PCHE is analyzed based on the results of optimization, which indicates that the variations of thermal-hydraulic parameters along the streamwise direction in FT-PCHE have a significant effect on the heat transfer efficiency and pumping power in the fractal-tree microchannels at the same working conditions. Furthermore, compared with the optimized conventional straight microchannel PCHE (SM-PCHE) also via the improved NSGA-II, the pumping power through the FT-PCHE is decreased by 26.5% at most than that through the SM-PCHE with the same level of total thermal resistance. The present study indicates that the proposed fractal-tree channel is an effective structure for printed circuit heat exchangers in next-generation nuclear power plants.