Autonomous planning robotic contact-rich manipulation has long been a challenging problem. Automatic peeling of glass substrates of LCD flat panel displays is a typical contact-rich manipulation task, which requires extremely high safe handling through the manipulation process. To this end of peeling glass substrates automatically, the system model is established from data and is used for the online planning of the robot motion in this paper. A simulation environment is designed to pretrain the process model with deep learning-based neural network structure to avoid expensive and time-consuming collection of real-time data. Then, an online learning algorithm is introduced to tune the pretrained model according to the real-time data from the peeling process experiments to cover the uncertainties of the real process. Finally, an Online Learning Model Predictive Path Integral (OL-MPPI) algorithm is proposed for the optimal trajectory planning of the robot. The performance of our algorithm was validated through glass substrate peeling tasks of experiments.