Accurate simulation of photovoltaic characteristics is now a mandatory obligation before validating an experiment; hence, accurate model and parameters of solar cells are indispensable. This paper presents an improved explicit double-diode model based on the Lambert W function (EDDM-LW), and then compares the fitness and parameter extraction performance. By defining two new parameters (K and r) to separate the exponential function in double-diode model (DDM) and using the Lambert W function, the explicit expression for I-V characteristics is proposed. In contrast to exiting works, the new parameters can readily be computed by the electrical characteristics of the standard test condition without an implicit characteristic. To verify the accuracy of the proposed model, the fitness difference is first investigated with a solar cell and three different types of solar modules. The results indicate that under the same parameter values, EDDM-LW achieves the lowest root mean square error value and exhibits better fitness in representing the I-V characteristics. In addition, the optimal parameters are extracted by an improved teaching-learning-based optimization algorithm. The experimental results show that the optimal parameter values extracted from EDDM-LW are more accurate than those extracted from DDM. Based on these observations, EDDM-LW can be deemed a useful and practical model for the simulation, evaluation, and optimization of the photovoltaic system.