The grey prediction models of time series are widely used in demand forecasting because only limited data can be used to build the models and no statistical hypothesis is needed. In this paper, a grey power Markov prediction model (RGPMM(λ,1,1)) with time-varying parameters is proposed. This model is based on the principle of “new information priority”, combined with rolling mechanism and Markov theory, and the prediction residual error is modified to further improve the prediction accuracy. Compared with the classic grey models, the new model not only overcomes the inherent defect of poor adaptability to the original data, but also uses real-time information to better reflect the nonlinear characteristics of the original data, so it can be used to describe and predict the nonlinear development trend of things. In order to verify the validity and applicability of the model, the proposed model is used to forecast the total electric consumption in China. The experimental results show that the proposed model has a better prediction effect than other grey models. The proposed model is used to forecast China’s total electricity consumption in the next six years from 2018 to 2023.