A lumped-parameter equivalent circuit model of organic solar cells (OSCs) is proposed to analyze the S-shaped current-voltage (I-V) characteristics and the explicit solution to I-V equation is derived so that this model is suitable to be compactly implemented for the simulations of photovoltaic applications. Comparing our explicit solutions with the method of least squares and the Newton-Raphson root-finding scheme, the simulations quantiflcationally reproduce the S-shaped I-V characteristics of OSCs especially for both linear- and exponential like S-shaped kink in the third and first quadrants, respectively. Simultaneously, the simulations facilitate us to qualitatively analyze the S-shaped I-V characteristics of OSCs influenced by the different model parameters. Furthermore, we verify the simulation results of our proposed model by using the reconstructed experimental data. Good agreements indicate that such a model can be used to accurately predict the S-shaped I-V characteristics of OSCs and regarded as a serviceable tool implemented compactly into simulations of the wide photovoltaic applications.