Accurate dynamic model and response prediction of industrial robots (IRs) are prerequisites for production optimization before actual operation. In this study, a hybrid-driven dynamic position prediction (HDPP) approach integrating a parametric dynamic model (PDM) and learning-based residual error compensators (RECs) is developed to estimate the actual position of a robot end-effector based on the reference input trajectory. Firstly, a PDM consisting of a flexible dynamic model of the mechanical system and a servo system model is constructed as the primary predictor in HDPP. Meanwhile, a reinforcement learning (RL)-based parameter identification method is presented to obtain independent dynamic parameters, which integrates a CAD model, least squares estimation, and RL. Then, an REC based on the temporal convolutional network long short-term memory (TCN-LSTM) is proposed for each joint to compensate for the residual error after PDM prediction. A TCN is employed as the input of LSTM to extract and compress the discontinuous features, which can enhance the compensator’s accuracy and stability. Additionally, a dynamics-integrated (DI) dataset construction scheme is developed for network training to boost the prediction accuracy. Finally, a series of experiments and comparative analysis are preformed to validate the performance of HDPP in terms of prediction accuracy and stability.