This paper presents an algorithm for Boundary Value Problems (B.V.P) defined on semi infinite interval approximately. Firstly, the problem is transformed into a new equivalent Volterra integral equation and then Hermite polynomials are used for solving V.I.E approximately with the aid of spectral method. The V.I.E reduces to linear system of algebraic equations with unknown Hermite coefficients'. Comparisons between the exact and approximated results of this method are given via two test examples and accurate results are achieved.