A numerical study is conducted to investigate supercritical hydrogen flow and heat transfer mechanisms and characteristics in printed circuit heat exchanger (PCHE) channels. The impact of large variations of the thermal-physical properties due to a wide range of operating temperatures have been studied and analyzed in detail. The heat transfer mechanisms of supercritical hydrgen under horizontal and vertical flow conditions are studied numerically. In addition, the influence of different cross-section shapes of the channel is also analyzed. The results show that asymmetrical fluid temperature distributions near the top wall and bottom wall due to the buoyancy effect result in heat transfer deterioration. Spiral flow occurs in the heat transfer deterioration region, which further confirms that the heat transfer deterioration is related to the spiral flow effect caused by the buoyancy effect. The heat transfer coefficient without gravity is lower than that with gravity, indicating that the buoyancy effect enhances the overall heat transfer in the horizontal circular channel. Furthermore, the fluid temperature in the vertical upflow channel decreases slowly from the near wall to the core area, while the fluid temperature in the vertical downflow channel changes sharply, which directly leads to the difference in the temperature gradient near the wall. Compared with the square cross-section channel and semicircular cross-section channel, the supercritical hydrogen can achieve greater heat transfer performance in the circular cross-section channel.