A methodology for the parameterization and inverse design of airfoils, for obtaining a given target surface pressure distribution is presented. The airfoil parameterization is carried out using ordered pairs representing the x-y coordinates of ten control points of Bezier curve as parameters. The forward model consists of analysis of flow over airfoils carried out using vortex element method, which involve discretisation of the airfoil curve alone, in contrast to complicated grid generation over the region of flow. The airfoil parameters are selected by global search using a Genetic Algorithm code. Examples to illustrate the parameterization and design of airfoils are presented. A good matching between the target and designed airfoil shows that present methodology can be used as a tool for the design of airfoils.