The energy ladder model and energy stacking model have been proposed in the literature to describe the relations between income growth and transition of energy consumed by households. Both models are largely descriptive and provide limited guidelines for quantitative verification. By contrast, the logistic substitution model has been adopted much earlier to depict the long-run energy transition of a society over time. This model assumes that substitute technologies in energy sources are available in the energy market. In the present paper, we argue that household energy transition over income can follow the same pattern as energy dynamics over time in the logistic substation model. Hence, we construct a new model, energy wave transition model, by adapting the logistic substitution model to describe household energy transition both over time and over income. The new model not only captures the features presented in the energy ladder and stacking models, but also provides methods for quantitative verification.We illustrate the new model using the energy consumption pattern of Chinese households as an example.