Due to the wide application of industrial robots (IRs) in the manufacturing industry and their significant energy consumption (EC), predicting EC under different trajectories and working conditions has attracted increasing attention. Data-driven modeling methods have proven to be a viable approach for revealing the quantitative relationship between IR operating parameters and EC. However, in manufacturing systems, the coexistence of numerous heterogeneous IRs necessitates a substantial amount of data with power labels and sufficient hardware computing resources to model the operational EC of each robot type. Motivated by these requirements, this paper proposes a transfer learning based method for modeling the operational EC of IRs. Based on an analysis of the temporal causal relationship between model input variables and operational EC, a time series information feature extraction method and an industrial robot operational energy consumption prediction network (ROEPN) are proposed, which combines layer normalization (LN), long short-term memory neural network (LSTM) and masked multi-head attention mechanism (MHA). Moreover, a rigorous pre-training-fine-tuning transfer learning scheme is designed and implemented on the target domain data, effectively achieving the transfer of ROEPN from the source domain to the target domain. Experiments were conducted on the HSR-JR612 and HSR-JR603, and the results demonstrate that the proposed EC model transfer method can predict EC for different IRs, trajectories and loads, with the mean absolute percentage error (MAPE) being less than 2.69% in the case of small samples.