Morphing airfoil is a promising technology for future aircraft to realize all-stage high performance. In the present paper, a conceptual aircraft with morphing airfoil is proposed and the aerodynamic characteristics of three types of morphing airfoils (variable-camber airfoil, variable-chord airfoil, and the combination of both morphing styles) are numerically investigated. The baseline airfoil is RAE 2822 supercritical airfoil; the Reynolds-averaged Navier–Stokes method is adopted for numerical simulation of flow around airfoils, and the accuracy of the numerical simulation method is validated by comparing with experimental data. It is found that the variable-camber and -chord airfoil can not only improve the high lift characteristics at take-off stage, but also increase the lift-to-drag ratio at transonic cruise and low-speed task stages during which the required lift is continuously decreasing due to the consumption of fuel. These findings imply that aircraft with proper morphing airfoil can achieve all-stage high aerodynamic performance.