In this paper, an analytical solution to three-diode lumped-parameter equivalent circuit model is proposed to simulate and present S-shaped I-V characteristics of next generation solar cells, which are observed frequently in perovskite and organic solar cells, and occasionally in other kinds of solar cells. In general, because complicated transcendental equation includes three exponent items resulting from three diodes, the absence of an analytical solution has become a bottleneck that limits the adoptions of solar cells' three-diode lumped-parameter model into practical applications and device simulations. To break through the above bottleneck, the analytical solution is derived in the regional approach, completed in Matlab platform, and verified by reconstructed experimental data measured from real solar cells. Such an analytical solution processes the key feature with high precise and efficiency. High precise results from the mathematical operations of the analytical solution to lumped-parameter model and high efficiency results from the avoidance of numerical iteration methods. In addition, this analytical solution facilitates researchers to accurately determine short circuit current and open circuit voltage, quickly extract model parameters in lumped-parameter circuit, and in detail assess effects from model parameters on DC characteristics of solar cells. Finally, the proposed analytical solution is able to be used to reproduce S-shaped I-V characteristics of solar cells, assist in extracting fitting parameters in three-diode lumped-parameter equivalent circuit model, and complete implementation of model into semiconductor device and circuit simulators.