Aerodynamic shape optimal designs for two- and three-dimensional wings are studied with the Euler equation on the structured grid. The Euler equation is solved using the Roe's 2nd-order Upwind TVD scheme and DADI time march. An optimal process is running through the gradient-based design method which is modified into the various methods; pseudo-time and multilevel design methods. To obtain the sensitivity of objective function, the adjoint method which is proved to be computationally efficient is employed instead of the finite difference method. The Hicks-Henne function, the Theodorsen transformation and the B-spline curve are used to embody the airfoil as shape functions. The drag minimization is applied to the three-dimensional wing expansively changing the wing sections and wing sweep. After the design, the aerodynamic property is shown to be better than before.