Due to wide distribution and low energy efficiency, the energy-saving in industrial robots (IRs) is attracting extensive attention. Accurate energy consumption (EC) models of IRs lay the foundation for energy-saving. However, most dynamic and electrical parameters of IRs are not disclosed by manufacturers, which leads to the invalidity of most model-based EC prediction methods. To bridge this gap, a mechanism-data hybrid-driven method is proposed to predict the EC of IRs in this paper. First, a joint torque prediction model integrating a hybrid-driven parameter identification is developed based on deep reinforcement learning (DRL). The framework for DRL-based parameter identification is constructed through tailored design of interfaces and training mechanisms, wherein the DRL agent can learn to identify the dynamic parameters from the trajectory database. And a deep neural network based on long short-term memory (LSTM) is proposed to predict the EC of IRs according to the joint torques and velocities. The nonlinear item, which is not modeled in the robot dynamic equation, are also encapsulated in the deep neural network with one-dimensional convolutional neural network (1D-CNN) layers to improve the prediction accuracy. To validate the accuracy and efficacy of the proposed method, experiments are conducted on a KUKA KR60-3 industrial robot with different loads. The results demonstrate that the proposed method can predict EC with a mean absolute percentage error of less than 2% under a fixed load and less than 3% under loads not used for agent training.