Abstract: This paper studies the admissibility of linear estimators in multivariate linear models with respect to an incomplete ellipsoidal restriction \mboxtr(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2. Specifically, we study the influence of the matrix N and \Theta_1 which is the center of a restricted set to the admissibility of linear estimators in multivariate linear models with respect to the incomplete ellipsoidal restriction \mboxtr(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2. The main results show that the class of admissible linear estimators with the restriction \mboxtr(\Theta-\Theta_1)'N(\Theta-\Theta_1)\leq\sigma^2 is the same as the one with the restriction \mboxtr(\Theta-\Theta_2)'N(\Theta-\Theta_2)\leq\sigma^2 for \Theta_1 and \Theta_2 with certain relationship.