The functional differential equation plays important role in mathematical modeling of biological problems. In the present research work, we investigate a boundary value problem (BVP) for a functional differential equation. This equation includes loaded terms and a term with generalized piecewise constant argument. We apply a modified version of the Dzhumabaev parameterization method. The method's goal is to lead the original problem into an equivalent multi-point BVP for ordinary differential equations with parameters, which is composed of a problem with initial and additional conditions. The multi-point BVP is leaded to a system of linear algebraic equations in parameters, which are introduced as the values of the desired solution at the dividing points. The found parameters are plugged into auxiliary Cauchy problems on the partition subintervals, whose solutions are the restrictions of the solution to the original problem. The obtained results are verified by a numerical example. Numerical analysis showed high efficiency of the constructed modified version of the Dzhumabaev parameterization method.