The objective of this paper is to estimate the values of five parameters ($A$, $R_{se}$, $ R_{sh}$, $ I_{LG}$, and $I_{sat})$ of a PV module more accurately and to extract the maximum power point (MPP) accurately under varying environmental conditions. Suitable new equations are proposed, by which the values of the series and shunt resistances are initialized in order to obtain good convergence speed in the Gauss--Seidel method. In this work, two new equations are proposed to find the ideality factor and shunt resistance and to obtain accurate MPP of the PV model under varying environmental conditions. The proposed PV model is validated at standard test conditions and under varying environmental conditions. Current--voltage and power--voltage characteristics of different PV modules are simulated using MATLAB. Accuracy of the proposed model is validated by comparing with the results of an adaptive neuro-fuzzy inference system and experimental data taken under varying environmental conditions.