The stability of a non-parallel flowfield over an airfoil has been investigated by applying a two-dimensional global (non-parallel) linear stability analysis. In this study, Chiba's method, which is a numerical method for the global linear stability analysis, was improved in order to study the stability of the time-averaged flowfield of CFD results. In a laminar separation bubble formed on the airfoil, a sequence of vortices is experimentally observed, which is generated by Kelvin-Helmholtz instability. By applying the stability analysis, we can examine the mode such as an oscillatory phenomenon that is generated by the instability of the flowfield. At higher angles of attack, a separated flow is observed at the leading edge of the airfoil, which corresponds to the stall condition of the airfoil. The results of the global stability analysis at high angles of attack demonstrate the mode which causes the separation at the leading edge of the airfoil. In this paper, the mode of Kelvin-Helmholtz instability and the mode which causes the stall condition of flowfield are presented.