•A novel discrete GM(2,1) model with a polynomial term is proposed.•The generalization and adaptability of the proposed model were validated from the theoretical and practical perspectives.•The newly-designed model is applied to predict per capita living electricity consumption. The forecast of electrical energy demand has played an increasingly relevant role in sustainable electrical power system. This paper develops a new method for forecasting China's per capita living electricity consumption by grey modelling technique. Considering the multiple and mixed change patterns, a novel discrete grey model with polynomial term (abbreviated as DGM(2,1,kn)) is proposed in this study. Firstly, the polynomial term is introduced into the discrete DGM(2,1) model. Secondly, the Tikhonov regularization method is employed to solve the overfitting problem. Lastly, two published cases and China's per capita living electricity consumption are used to validate the generalization and adaptability of the newly-designed model. The numerical results of such experiments show that the proposed model outperforms other competitive models in terms of accuracy level. Therefore, the projections of China's per capita living electricity consumption in 2020 and 2025 have been made for providing a solid reference for the formulation of electrical power strategies.