In this paper, we address the open problem on the James-Stein estimation for multivariate linear regression models. Under the canonical risk function or the mean-squared error, we derive an oracle James-Stein estimator, present an adaptive James-Stein estimator and propose the concepts of left and right James-Stein estimators for multivariate situations. We claim and prove the nonexistence of the traditional James-Stein estimator for multivariate situations in the whole parameter space. We also provide the lower bound of the risk for all James-Stein type decisions. As a substitute of the James-Stein estimator, we construct a combination estimator for mean matrix for multivariate linear regression models by absorbing the advantages of left James-Stein and modified Stein estimators. The risk comparisons through finite sample simulation studies illustrate that the proposed combination estimator has a much better risk than the existing estimators. A real data set is analyzed to demonstrate the proposed methodology.