The linear quadratic regulator with a low-pass property is well known as a high performance control system to suppress the spillover instability caused by residual modes. However, trial-and-error testing for selecting weighting matrices in linear quadratic regulator designs with the desired low-pass property is required. In this paper, a synthesis method of the linear quadratic regulator with the desired low-pass property is proposed. The basic design idea is based on the fact that feedback control law can be reduced to the problem which solves a quartic algebraic equation.