Abstract: Aiming at the problems of insufficient adaptability and limited prediction accuracy of traditional grey prediction model in the application of complex nonlinear system, we provide a novel generalized fractal grey model in this study. Firstly, we innovatively construct a new difference operator called fractal difference. Then, based on this operator, a generalized fractal grey prediction model with exponential kernel (GFGM) is proposed, and the hyper-parameters of GFGM are accurately solved by intelligent optimization model. The model is more adaptable and able to describe complex data patterns more accurately. Finally, we apply the model to the prediction of graduate education scale, and the experimental results show that the GFGM model demonstrates higher accuracy and superiority compared to other traditional models. This study provides an efficient and accurate new tool for predicting complex systems.