Abstract: In this paper, we study the Seemingly Unrelated Regression Model with design matrices have same range space. We give the necessary and sufficient conditions that a linear estimator of regression coefficient is lenear admissible under matrix loss. The results generalize t;he conclusions got before by others. We also give a unique linear minimax estimator of regression coefficient in a regression model under matrix loss.It shows that the information of other models doesn’t play a role in estimation.