Abstract: In the simulation and design calculations of photovoltaic (PV) systems, it is very crucial to select an accurate mathematical model to closely represent the nonlinear current-voltage (I-V) characteristics of solar cells. In practice, two main equivalent circuit models are used widely: the single and double diode models. The single diode model contains five unknown parameters, while the double diode model has seven unknown parameters, which are not always available in commercial PV datasheets. Hence, parameter extraction of solar cell models is an essential prerequisite for the precise modeling, performance analysis, and optimal control of PV systems. Unfortunately, since the single and double diode models are inherently implicit and transcendental in nature, it is difficult to quickly and accurately identify their unknown parameters just by analytic methods or traditional numerical optimization methods. By combining an approximate analytic method and the Nelder-Mead simplex method (NM), an comprehensively hybrid algorithm named A-bcNM is proposed in this paper to simultaneously determine the precise values of photo-generated current, diode saturation currents, parasitic series and shunt resistances, and diode ideality factors of solar cell models. In the A-bcNM method, the parameter identification problem of solar cell models is formulated as a bounded, multidimensional, nonlinear optimization problem of minimizing a given objective function. The basic idea of the A-bcNM method can be broken up into three phases. First, we make use of several key points on the nonlinear I-V characteristic curve to roughly estimate the synthetic parameters, i.e., the output current and voltage at the maximum power point, short-circuit current, open-circuit voltage, and slopes of the I-V characteristic at the axis intersections. Secondly, we substitute the synthetic parameters into our proposed approximate analytical formulas of the single diode model so as to quickly pinpoint the initial search point for the NM method. The third phase of A-bcNM is utilizing the NM method as optimizer to minimize the root mean square error between the experimental data and the simulated data, and restart the NM method at the currently observed points several times. The main intention of restarting the NM method is to escape from the local extreme points and further improve the precision of fitting and the quality of parameter solutions. To evaluate the speed of convergence and accuracy of the A-bcNM method presented here, single and double diode models of two typical solar cells were tested. The identification results indicate that the simulation data with the parameters obtained by A-bcNM method are in very good agreement with the experimental data in all cases. Comparing with the best known methods reported in the literature, such as a genetic algorithm (GA), simulated annealing (SA), pattern search (PS), particle swarm optimization (PSO), harmony search (HS), artificial bee swarm optimization (ABSO), improved adaptive differential evolution (IADE), bird mating optimizer (BMO), and repaired adaptive differential evolution (Rcr-IJADE), all cases demonstrate that the A-bcNM method is rather simple, straightforward, computationally efficient and sufficiently accurate for parameter identification of solar cell models. In short, simple concept, easy implementation and high performance are the main advantages of the A-bcNM method, and it is useful for PV systems designers to build an efficient and accurate solar cell system simulator.