On the basis of the variational principles developed in Ref[1], a finite element method(FEM) is constituted for soluting the inverse problem of 2-D unsteady transonic flow around oscillating airfoils, incorporating the non-reflecting far-field boundary conditions and a new unsteady Kutta condition^[7]. All unknown boundary(airfoil contour) and discontinuities(shocks and free trailing vortex sheets) are handled(captured) via the functional variation with variable domain and artificial density concept. For the numerical realization of variable-domain variation, a special finite element with self-adjusting nodes is also suggested herein. The numerical results show that the present method is effective for the design of unsteady airfoil.