This paper deals with a class of optimal control problems governed by linear Fredholm integral equations. A direct scheme based on the Taylor expansion and parametrization to calculate an approximate-analytical solution of the problem is proposed. This method produces an approximation with a controlled level of accuracy. Moreover, a hybrid algorithm to show the procedure of the scheme is given. The convergence of the proposed scheme is also discussed in detail. Some numerical examples illustrate the potential, efficiency and accuracy of the algorithm.