Shifted Legendre polynomials are applied to solve the state equations of linear system. The computation procedure is greatly simplified by introducing the operational matrix for the integration of shifted Legendre vectors whose elements are shifted Legendre polynomials. The key of the method is that the state and forcing functions are expressed in terms of a series of shifted Legendre polynomials with expansion coefficients. Ordinary differential equations of state system are transformed into a series of algebraic equations of the shifted Legendre expansion coefficients and then are solved by employing the technique of matrix inverse. The methods of the computational algorithms are also investigated in order to simplify the calculation procedure and make the calculation convergent.