In engineering design, according to not considering past experience information; hence, to make structure parameters for achieving high confidence level, much data for traditional reliability-based robust design must be adequately collected, analyzed, and tested. However, in practical engineering, it is very difficult for doing much test, only for getting in the form of finite test samples. Under the conditions, it has much difficult for the traditional reliability-based robust design. In the article, we present a new reliability-based robust design method that solves the form of incomplete information. The method adopts a Bayesian inference technique to estimate reliability, gives definition of Bayesian reliability. In the research, the mechanical parts bayesian reliability-based robust design mathematical model is established and the bayesian reliability-based robust design approach is presented. The numerical results illustrates the method presented is an efficient and practical reliability-based robust design approach.