Vehicle weight reduction has become one of the most crucial problems in the automotive industry. Increasingly stringent regulatory requirements, such as fuel economy and environmental protection, must be met. The lightweight design needs to consider various vehicle attributes, including crashworthiness and stiffness. Therefore, the essence of vehicle weight reduction is a typical Multidisciplinary Design Optimization problem. To improve the computational efficiency, meta-models have been widely used as the surrogate of FE model in the multidisciplinary optimization of large structures. However, these surrogate models introduce additional sources of uncertainty, such as model uncertainty, which may lead to the poor accuracy in prediction. In this paper, a method of corrected Surrogate model based multidisciplinary design optimization under uncertainty is proposed to incorporate both of the uncertainties introduced by meta-models and design variables. Firstly, various meta-models are constructed and the meta-models with the highest accuracy are selected to serve as the surrogates of FE model. Followed by the evaluation of corresponding model bias of the selected models. Then the Gaussian Process model for the bias function is built and employed to correct the previously built low fidelity meta-model for the reason that Gaussian Process Regression, a kind of nonparametric probabilistic model, can quantify the uncertainties introduced by the usage of the meta-model. Finally, based on the non-dominated sorting genetic algorithm II (NSGA-II), robust solution which can meet the performance requirements of different subjects is found efficiently. The proposed method is demonstrated through a vehicle weight reduction problem while satisfying safety and NVH performance requirements.