We present a derivative-enhanced Gaussian Process Regression surrogate model designed for aerodynamic design optimization. The proposed model can incorporate arbitrary directional derivatives of an objective function alongside the functional values during model training. By leveraging this additional derivative information, the surrogate model is better equipped to capture the true tendencies in the data, effectively mitigating the issue of over-exploration commonly encountered in the Bayesian optimization framework. This approach ensures more accurate and reliable predictions, ultimately enhancing the efficiency of the optimization process. The proposed framework was tested on a generic shape optimization problem, specifically the drag minimization of the RAE2822 airfoil under lift and cross-sectional area constraints. The results demonstrated a significant improvement in the convergence rate of the optimization process when gradient evaluations were selectively used.