An efe cient aerodynamic design optimization method for the compressible Euler equations is presented. A gradient-based optimization method is used to e nd the optimal design, in conjunction with a continuous adjoint sensitivity analysis method. To improve the efe ciency of the design method, a tightly coupled algorithm based on a step-size estimation isproposed. The efe ciency of thepresentmethod is demonstrated through drag minimizations of a wing and an airfoil. The result shows that the cost of the present method is signie cantly lower than that of the loosely coupled algorithm. Nomenclature Ci = e ux Jacobian matrix in the computational domain d = design variables vector Fi = e ux vector in the computational domain fi = e ux vector in the physical domain G = gradient vector of the object function I = object function q = conservative e ow variables vector R = residual vector in the computational domain S = searching direction ≤ = step size along the searching direction S A = Lagrangian multiplier vector Subscript face = value at cell face Superscript T = transpose of vector or matrix