A new method for inverse problem of two dimensional unsteady flow around oscillating airfoils is proposed, by solving unsteady Euler Equations in mapping coordinates. The unsteady boundary conditions and the schemes to solve unsteady inverse problem are given. The approach can unify the subsonic, transonic and supersonic inverse problems and avoid the direct simulation of the unsteady wake of oscillating airfoil. The problem about the uncertainty of airfoil geometry is settled by coordinate transformation in the paper.