The operational matrix of backward integration for the shifted Chebyshev polynomials is introduced in this study. The general expression of the shifted Chebyshev polynomial approximation for any two arbitrary functions is also presented. A linear time-varying optimal control system with a quadratic performance measure is solved by using the shifted Chebyshev polynomials. Only a small number of Chebyshev polynomials is needed to produce an excellent result, and the outcome is much better than the solution obtained by using the block-pulse function. So, computer memory capacity and computing time can be saved considerably.