This paper is devoted to the numerical analysis of the recently obtained theoretic results for a class of optimal control processes governed by Volterra integro-differential equations (see [5]). Using the specific structure of the delayed Volterra integro-differential equations under consideration, we reduce the initially given Optimal Control Problem (OCP) to a numerically tractable separate convex-concave program. This reduction involves optimization techniques in real Hilbert spaces and makes it possible to apply the first-order solution algorithms to the sophisticated Volterra type OCPs. We next consider the celebrated Armijo gradient method for the purpose of a concrete computation and establish the numerical consistency of the resulting algorithm. Finally, we consider an illustrative example.