To reduce the computational time of the iterations in robust design, meta-models are frequently utilized to approximate time-consuming computer aided engineering models. However, the bias of meta-model uncertainty largely affects the robustness of the prediction results, this uncertainty need to be addressed before design optimization. In this paper, an efficient uncertainty quantification method considering both model and parameter uncertainties is proposed. Firstly, the uncertainty of parameters are characterized by statistical distributions. The Bayesian inference is then performed to improve the predictive capabilities of the surrogate models, meanwhile, the model uncertainty can also be quantified in the form of variance. Monte Carlo sampling is finally utilized to quantify the compound uncertainties of model and parameter. Furthermore, the proposed uncertainty quantification method is used for robust design. A numerical example and a real-world vehicle lightweight case study are used to demonstrate the validity of the proposed method.