Abstract: In recent years, reduced-rank models have attracted considerable attention in multivariate response regression models. Rank selection is of importance in the research on reduced-rank models. However, existing literature generally achieves low-rank coefficient estimation based on some information criteria or penalized nuclear norm methods on coefficient matrix. However, when data contain outliers or the model is complex, the accuracy of rank selection tends to be low. To account for data uncertainty and enhance model adaptability, this paper introduces a Bayesian robust estimation method for mixed low-rank models by incorporating a drift coefficient inspired by the model averaging idea, and provides a maximum posteriori (MAP) estimation for the parameters by combining the Bayesian hierarchical model and the EM algorithm. Extensive numerical simulations and comparisons with existing methods demonstrate the effectiveness and robustness of the proposed method, which is further validated through an application on the Seattle traffc accident dataset.