This paper is devoted to the approximate solution of a linear first-order functional differential equation which involves delayed and advanced arguments. We seek a solution x, defined for t???(0, k???1],(k???IN ), which takes given values on the intervals [???1, 0] and (k???1, k]. Continuing the work started in previous articles on this subject, we introduce and analyse a computational algorithm based on the finite element method for the solution of this problem which is applicable both in the case of constant and variable coefficients. Numerical results are presented and compared with the results obtained by other methods.