Reliability-based design optimization (RBDO) has been widely used to obtain a reliable design via an existing CAE model considering the variations of input variables. However, most RBDO approaches do not consider the CAE model bias and uncertainty, which may largely affect the reliability assessment of the final design and result in risky design decisions. In this paper, the Gaussian Process Modeling (GPM) approach is applied to statistically correct the model discrepancy which is represented as a bias function, and to quantify model uncertainty based on collected data from either real tests or high-fidelity CAE simulations. After the corrected model is validated by extra sets of test data, it is integrated into the RBDO formulation to obtain a reliable solution that meets the overall reliability targets while considering both model and parameter uncertainties. The proposed technique is demonstrated through a vehicle design problem aiming at minimizing the vehicle weight through gauge optimization while satisfying reliability constraints. The RBDO result considering model uncertainty is compared with the one from conventional RBDO to demonstrate the benefits of the proposed method.