A corrected Mahalanobis Mallows model averaging ( MMMAc) method was proposed for the multivariate response linear regression model. In order to make full use of the correlation information among multivariate response variables and improve the prediction accuracy, Mahalanobis distance prediction risk was also considered in the construction of combinational weight selection criteria. And by constructing the Wishart distribution, the unbiased estimate of predicted loss was derived as the selection criterion of weight. Compared with the original MMMA criterion, the resulting MMMAc added a bias correction term, which reduced the bias in the prediction loss estimation. Therefore, the weight estimation obtained by minimizing this criterion was closer to the theoretical optimal combination weight that is not available. Finally, the simulation and comparison experiments verified the advantages of the MMMAc method: the MMMAc estimation has the same asymptotic optimality as the MMMA estimation, so there is no significant difference in their performance in the large sample case; however, since the modified weight selection criterion is an unbiased estimate of the prediction loss, the MMMAc method performs better in the case of insufficient sample size.