A surrogate-based optimization algorithm for transonic airfoil design is presented. The approach replaces the direct optimization of an accurate, but computationally expensive, high-fidelity computational fluid dynamics model by an iterative reoptimization of a physics-based surrogate model. The surrogate model is constructed, during each design iteration, using the low-fidelity model and the data obtained from one high-fidelity model evaluation. The low-fidelity model is based on the same governing fluid flow equations as the high-fidelity one, but uses coarser mesh resolution and relaxed convergence criteria. The shape-preserving response prediction technique is utilized to predict the high-fidelity model response, here, the airfoil pressure distribution. In this prediction process, the shape-preserving response prediction employs the actual changes of the low-fidelity model response due to the design variable adjustments. The shape-preserving response prediction algorithm is embedded into the trust region framework that ensures good convergence properties of the optimization procedure. This method is applied to constrained airfoil lift maximization and drag minimization in two-dimensional inviscid transonic flow. The optimized designs are obtained at lower computational cost than that of two comparators. The robustness and scaling properties of the proposed algorithm are investigated.