Abstract: Let Y be a random n-vector with mean Xβ and covariance matrix σ²V, and Sβ be a linear estimable function, where X, S and V≥ 0 are known matrices, β∈ R^P and σ² ＞ 0 are unknown parameters. In this paper under the given matrix loss function and quadratic loss function, the minimax property of linear estimators is studied respectively. Under suitable hypotheses, we obtain the unique linear minimax estimator of Sβ（We must comprehend uniqueness in the sense " almost everywhere "）.