In the last decade, considerable advances have been made in reliability-based design optimization (RBDO). One assumption in RBDO is that the complete information of input uncertainties are known. However, this assumption is not valid in practical engineering applications, due to the lack of sufficient data. In practical engineering design, information concerning uncertainty parameters is usually in the form of finite samples. Existing methods in uncertainty based design optimization cannot handle design problems involving epistemic uncertainty with a shortage of information. Recently, a novel method referred to as Bayesian Reliability-Based Design Optimization (BRBDO) was proposed to properly handle design problems when engaging both epistemic and aleatory uncertainties . However, when a design problem involves a large number of epistemic variables, the computation task for BRBDO becomes extremely expensive. Thus, a more accurate and more efficient reliability method is demanded for BRBDO. In this article, the recently proposed Eigenvector Dimension Reduction (EDR) Method will be used for BRBDO in order to increase its accuracy and efficiency. When using the EDR method to carry out Bayesian reliability analyses, the accuracy and efficiency are substantially improved. Two design examples involving both aleatory and epistemic variables are used to demonstrate the accuracy and efficiency of BRBDO integrating with the EDR method.