The modified Hermite polynomials series solution of a functional differential equation of scaled systems is obtained. The Hermite polynomials are modified from the conventional ones by using an additional parameter. In order to simplify the computational algorithm, the stretch operational matrix of the modified Hermite polynomials is introduced to solve such a functional differential equation. The key method is that the dependent variable is expressed by an infinite series of the modified Hermite polynomials. The expansion coefficients of the series are solved by the proposed effective computational algorithm, in which only one matrix inversion is required. An illustrative example is given. Very satisfactory computational results are obtained.