Motor power calculation plays an important role in ensuring production safety, formulating rolling schedule, and leveraging equipment capabilities. In order to improve calculation accuracy, a motor power prediction model combining mechanism model and data-driven method was proposed. The mechanism model was analytically solved by upper bound method, and then parts of the power analytical solutions (plastic deformation power, tension power, and shear power) and related variables were input into long short-term memory (LSTM) network for training, so as to extract depth characteristics and temporal correlations between variable data. Results show that the relative error of the proposed time series coupling prediction model was less than ±3.9%, and the prediction effect was obviously better than that of the upper bound method and artificial neural network (ANN) when the rolling schedule of adjacent strips changed greatly. According to the residual distribution histogram, the residual of upper bound method was concentrated around ±50 kW and deviating from a normal distribution, as it ignored the strong relationship between friction coefficient, loss power, and other parameters. Both ANN and the proposed model basically followed normal distribution, but the proposed model had higher fitting accuracy. In comparison with broader model evaluation indicators, the proposed model had better comprehensive prediction performance. Besides, the relationship between motor power, rolling length, and rolling speed was analyzed based on model output results, which indicated that the model not only has high prediction accuracy, but also strong consistency with known physical law between parameters.