The main cryogenic heat exchanger is a core piece of equipment in the liquefaction of natural gas. The printed circuit heat exchanger is gradually becoming a primary choice for the main cryogenic heat exchanger, because it has good pressure resistance, high efficiency, and compactness. In this work, a numerical simulation is conducted to examine the local flow and heat transfer characteristics of natural gas in the printed circuit heat exchanger during trans-critical liquefaction. It is found that the heat flux density reaches a minimum value and the heat transfer is the worst when the temperature difference between the hot and cold sides is the smallest. Owing to the large variations in physical properties of trans-critical natural gas, the local pressure drop exhibits an upward parabolic shape along the flow direction, and the pressure drop reaches a minimum value near the pseudo-critical point. Finally, the friction factor and heat transfer correlations for natural gas during trans-critical liquefaction are fitted.