Abstract: In this paper, the best linear unbiased estimator of regression coefficients in the linear model is studied. Under weighted balanced loss function the minimum risk properties of linear estimator of regression coefficients in the class of linear unbiased estimator is discussed. Furthermore, some kinds of relative efficiencies of the best linear unbiased estimator and ordinary least squares estimator are given, and the lower bound or upper bound of these relative efficiencies are also given.