•An efficient UBDO framework based on the proposed MF PC-Kriging model was developed.•The construction principle of the MF PC-Kriging model was explained reasonably.•The superiority of the MF PC-Kriging for building a surrogate for combined DV and RV was validated.•The developed method for transonic aerodynamic applications was proved to be reliable and efficient. Surrogate model has been extensively employed in uncertainty-based design optimization (UBDO) for computationally expensive engineering problems. However, it often causes great difficulties to designers due to the unsatisfactory accuracy and the high sensitivity of surrogate prediction in presence of uncertainties. Worse still, some popular metamodeling methods also require a substantially higher computational cost than that in deterministic design to get an acceptable accuracy. To address the challenging problem, an UBDO framework based on the proposed multi-fidelity polynomial chaos-Kriging (MF PC-Kriging) surrogate model is proposed, with particular superiority for complex aerodynamic applications. The construction principle of the MF PC-Kriging model and the rationality of the superiority of it with respect to popular surrogate models are explained in detail. Meantime, it is examined by investigating an analytical function and a transonic aerodynamic application with both geometrical and operational uncertainties. Thus, the MF PC-Kriging with easier understanding and better modeling capabilities is involved in UBDO to resolve the proposed difficulty. Finally, an uncertainty-based aerodynamic design optimization problem is performed using this proposed framework. It is observed that for the considered examples, the developed methodology is more efficient and provides the better performance for aerodynamic uncertainty analysis, and complex aerodynamic analysis and optimization under uncertainty compared with universal Kriging and PC-Kriging methods.