We use Isogeometric Analysis as a framework for NURBS-based shape optimization of hydrofoils. We present geometrical representations by NURBS and some of their properties to design an hydrofoil. Then, we consider an irrotational flow around an hydrofoil and solve the Laplace equation in the stream function formulation. Finally, we perform the shape optimization of the hydrofoil by considering the stream function formulation as the state problem and different objective functionals.