To improve solar energy efficiency and reduce the dependence on fossil fuels, accurate parameter extraction and modelling of Photovoltaic (PV) cells are needed to achieve optimal design and control. However, the highly nonlinear and multi-modal characteristics of PV cells make traditional optimization methods inadequate to obtain an optimal solution. In addition, insufficient measured current-voltage (I-V) data also leads to imprecise modelling. Therefore, a Data Prediction-based Meta-Heuristic Algorithm (DPMhA) is proposed to realize the parameter extraction from a PV cell. In particular, an Extreme Learning Machine (ELM) is used to train and predict measured data, so as to provide a more accurate and reliable fitness function for the algorithm. Then global exploration and local exploitation can be simultaneously enhanced. Finally, a PV cell model with double diodes is employed to identify unknown parameters. Case studies show that DPMhA has advantages of high accuracy and fast convergence. This work is supported by the National Natural Science Foundation of China (No. 52067004) and the Science and Technology Project of Guizhou Power Grid Co., Ltd. (No. 066600KK52180051).