Abstract: In control system desigm the steady-state error is a very important design index. Using the freedom of the state-weighting matrix Q in the quadratic performance index, we propose a method for designing the linear quadratic optimal control systems with the least steady-state error. The formula for computing the gradient matrix of the steady-state error index corresponding to the matrix Q has been derived, and the design algorithm, which uses Beale's algorithm and Anmijo's rule in the conjugate gradient optimizing method to determine the optimizing direction and step-size and is easily implemented on computer, is also presented. The validaty of the design method is verified by simulation examples and many useful results are obtained.