This paper presents an algebraic approach to optimal control for time invariant continuous system using STWS(single term Walsh series). In optimal control, it is well known that the design problem with quadratic performance criteria often involves the determination of time-varying feedback gain matrix by solving the matrix nonlinear Riccati equation and of command signal by solving the integral equation, which makes design procedure quite difficult. Therefore, in order to resolve this problem, this paper is introduced to STWS. In this paper, the time-varying feedback gains and command signals are determined by piecewise constant gains which can be easily obtained from algebraic equation using STWS.