Gurney flap is a simple and effective high-lift device that has the potential to reduce the takeoff-and-landing distance for transport aircraft. It is also a good option for enhancing the airfoil cruising characteristics. However, its effectiveness in non-continuum regimes has rarely been studied. The Unified Gas Kinetic Scheme algorithm, which is valid for all flow regimes, is further developed and used to simulate the flow field around a cambered airfoil and a high-speed quadrilateral airfoil with and without the Gurney flap in the supersonic non-continuum flow regimes. The distribution function shapes at different spatial locations are provided and analyzed. The effects of angle of attack, free-stream Knudsen number, free-stream Mach number, Gurney flap height, and Gurney flap mounting angle on the aerodynamic characteristics of the two airfoils are studied. The results show that the lift and drag of the airfoil with the attached Gurney flap are increased. The pressure rise on the lower surface of the airfoil is the primary factor contributing to the increase in lift. The overall increase in drag mainly comes from the Gurney flap, which also generates a small amount of negative lift. When the angle of attack is less than the critical angle of attack, the Gurney flap can increase the lift-to-drag ratio of the airfoil and improve its aerodynamic performance. The critical angle of attack decreases with the increase in the free-stream Knudsen number and the free-stream Mach number. It decreases with increasing Gurney flap height and increases with increasing Gurney flap mounting angle.