The multi-fidelity surrogate-assisted global aerodynamic optimization method has become one of the most efficient means to improve the efficiency and reliability of surrogate-based optimization algorithms. However, currently popular multi-fidelity surrogate models, e.g., co-Kriging and hierarchical Kriging (HK) models, lack the generalization ability and the adaptability to complex engineering applications, so that it is very difficult to promote them to be widely utilized. In this paper, based on the developed adaptive multi-fidelity polynomial chaos-Kriging (MF-PCK) surrogate model, an efficient global aerodynamic optimization framework based on the novel adaptive MF-PCK model is proposed while improving the modeling efficiency and the global approximation accuracy for highly-nonlinear and high-order response problems. In the development framework, we proposed a new adaptive multi-fidelity polynomial chaos-Kriging-based variable-fidelity expected improvement (MF-PCK-VF-EI) infilling strategy that can adaptively select new samples of both low- and high-fidelity, which further improves the efficiency and ability of this optimization framework. The developed methodology is verified by one analytical function example and demonstrated by three engineering application problems, including the deterministic optimization and the robust design optimization of several transonic aerodynamic shapes, compared with the popular Kriging-based and HK-based optimization algorithms. The results show that the global aerodynamic optimization efficiency of the developed method based on the novel adaptive MF-PCK model is higher than that based on the HK model and more than twice that based on the Kriging model, meantime with better and more reliable results. More importantly, the efficiency and performance of robust aerodynamic design optimization (RADO) for transonic aerodynamic shapes are prone to satisfy the requirements for complex engineering applications, which proves a significant advantage of the developed method over the popular Kriging-based and HK-based optimization algorithms.