An efficient optimization design method for transonic airfoils is developed by coupling the direct search EXTREM optimization method to a reliable aerodynamic analysis method.The aerodynamic analysis method is based on combination of full potential and viscous boundary layer flow analysis including calculations of laminar and turbulent boundary layers

natural or fixed transition prediction and separation prediction.The drag coefficient at design Mach number is considered as objective function and a set of smooth shape functions are adapted to fitting the basic goemetry.By using the numerical optimization method

supercritical airfoils or conventional low speed airfoils can be modified to be transonic airfoils which have the lower drag coefficient at transonic speeds.The presented method is attractive for practical engineering application because of its quick convergence.