We are interested by the general problem consisting of minimizing a functional of a state field solution of a PDE state equation. In Particular in this work, we optimize a 3D wing shape immersed an in inviscid flow to reduce drag. Whence, each evaluation of the cost functional is computationally expensive. For improving the convergence rate of the optimization algorihm, we propose a multi-scale algorithm inspired from the Full Multi-Grid method [1], and referred to as the Full and Adaptive Multi-Level Optimum-Shape Algorithm (FAMOSA), originally defined in [5]. The proposed method include the following strategies: • The simplest scheme " one way up " by choosing the parametrization of Bézier type to construct a hierarchy of embedded parametric spaces, via the classical degree elevation process [3]. • V-cycle algorithm by using (on the coarse level) " perturbation " unknowns from the latest fine estimate, i.e deformation instead of shapes.