A lumped-parameter equivalent circuit model is proposed to simulate the S-shaped current–voltage ( ${I}$ – ${V}$ ) characteristics exhibited in organic solar cells. First, we derive an explicit terminal current solution as a function of terminal voltage from the equation set of the three-diode lumped-parameter model proposed by Mazhari. Second, we improved Mazhari’s model to improve the accuracy and developed the explicit solution of our improved model to improve the efficiency. Third, we use the method of least squares, Newton–Raphson root-finding scheme, and experimental data to validate the solutions of Mazhari’s and our models. As a result, owing to high accuracy and efficiency of computation, our explicit calculation scheme, regarded as a useful tool, can help to implement Mazhari’s and our models into photovoltaic device and system simulators in compact format.