When discussing the commercial applications of photovoltaic (PV) systems, one of the most critical problems is to estimate the efficiency of a PV system because current (I) – voltage (V) and power (P) – voltage (V) characteristics are highly non-linear. It should be noted that most of the manufacturer’s datasheets do not have complete information on the electrical equivalent parameters of PV systems that are necessary for simulating an effective PV module. Compared to conventional approaches, computational optimization and global research strategies are more acceptable as an effective alternative to parameter estimation of solar PV modules. Recently, a Gradient-based optimizer (GBO) is reported to solve the engineering design optimization problems. However, the basic GBO algorithm is stuck in local optima when handling complex non-linear problems. In this sense, this paper presents a new optimization technique called the Chaotic-GBO (CGBO) algorithm to derive the parameters of PV modules while offering precise I-V and P-V curves. To this end, the CGBO algorithm is based on a chaotic generator to obtain the PV parameters combined with the GBO algorithm. There are five case studies considered to validate the performance of the proposed CGBO algorithm. A quantitative and qualitative performance evaluation reveals that the proposed CGBO algorithm has improved results than other state-of-the-art algorithms in terms of accuracy and robustness when obtaining PV parameters. The average RMSE values and runtime of five case studies are equal to 9.8427E-04, 2.3700E-04, 2.4251E-03, 4.3524E-03 and 1.8349E-03, and 18.44, 17.78, 18.18, 18.28 and 17.97, respectively. The results proved the superiority of the proposed CGBO algorithm over the different selected algorithms. For future research, this study will be backed up with external support at https://premkumarmanoharan.wixsite.com/mysite.