In this paper, the shifted Chebyshev polynomial functions approximation is extended to solve the linear ordinary differential equation of the two-point boundary-value problem. The linear ordinary differential equation of boundary-value problems are reduced to the linear functional differential equation of the initial-value problem. A new time-domain approach to the derivation of a Chebyshev transformation matrix is presented. Using the derived Chebyshev transformation matrix together with the Chebyshev integration matrix, the solution of the linear functional ordinary differential equation of initial-value problem can be obtained via shifted Chebyshev series. Two examples are given and the satisfactory computational results are compared with those of the exact solution.