The paper deals with the parameter estimation of InGaP/GaAs/Ge multi-junction solar cell and is based on minimizing the difference between the measured I–V and the theoretical I–V characteristics—the objective function. The parameter estimation was first performed on a multi-junction solar cell represented by a single-diode model containing eight parameters: five conventional parameters and three additional parameters for the negative diode breakdown voltage. An extended model is also presented for detailed analysis of the multi-junction cell containing three subcells connected in series. In this model, each subcell is represented by eight parameters, and therefore a total of 24 parameters describe the cell. The parameter estimation procedure requires derivatives of the first and the second order of an objective function, filtering of noisy measurements, iteration algorithm, guessing of initial parameters, zero finding, and stopping criteria. The paper presents a mathematical method and a procedure for extracting solar cell parameters based on I–V measured data. The parameters' values may be used for analysis of the current mismatch of the subcells, the power loss, the output power of the multi-junction cell for different environmental conditions, and to some extent, for cell fabrication. Copyright © 2012 John Wiley & Sons, Ltd.