This paper presents an approach for the control of linear systems with parameter uncertainty. The parameter uncertainty under consideration is assumed to be unknown but bounded and can exist in both state and input matrices. Using the linear quadratic optimal control formulation, we consider a cost functional which is parameterized by uncertainties. An upper bound on the cost which is incurred by state feedback control and system uncertainties is obtained, and a linear state feedback law is found to minimize the upper bound. Furthermore, under the conditions presented in this paper the steady-state bound-minimizing control gain is shown to exist and the stability of the resultant closed-loop systems is guaranteed for all admissible uncertainties. Finally, a gradient search algorithm is proposed to find the optimal values of the free parameters which affect the cost upper bound. A numerical example is included to demonstrate the effectiveness of the proposed method.