The paper is a multi-input generalization of the robustness result on the optimality of a linear-quadratic optimal control for a single-input system. The robust optimality of an optimal control is defined as its invariant optimality in the usual sense of minimizing some quadratic cost under the presence of small plant parameter variations. A necessary and sufficient condition for robust optimality of a given multi-input optimal control is derived first. Based on this result, a choice of the weighting matrix in the cost is proposed such that the resulting optimal control is robustly optimal. Both conditions can also be expressed as simple constraints on the zeros of some rational matrices related to the given optimal control or the associated weighting matrix, and thus are very easy to understand. The difference is also discussed between the results obtained for the multi-input case and those known for the single-input case.