A method for solving the linear ordinary differential equations of the two-point boundary-value problem using polynomial series is discussed. The linear ordinary differential equation of the two-point boundary-value problems are reduced to the linear functional differential equation of the initial value problem. It is known that any polynomial series basis vector can be transformed to Taylor polynomials by the use of a suitable transformation and Taylor series have the simplest operational properties. The solution of linear two-point boundary-value problems via Taylor series is first obtained and this solution using other polynomial series is then calculated by transforming the properties of the Taylor series to other polynomial series. The method is simple and convenient for digital computation. Illustrative examples are given.