Abstract: The energy consumption system represents a complex, nonlinear, and chaotic system. Starting from multiple nonlinearities within the energy consumption chaotic system. In this paper leverages the characteristics of the Lorenz chaotic system to establish multiple nonlinear differential equations that embody the features of the energy consumption system. Simultaneously, by utilizing the grey differential information inherent in differential and difference equations, a multivariate grey prediction model based on the energy consumption chaotic system is developed. This model not only organically integrates the nonlinear chaoticity of the system with the prediction accuracy of grey prediction models, enabling the simple grey prediction model to reflect the chaotic nature of the energy consumption system, but also meets the adaptive prediction requirements of the energy consumption system and addresses the challenge of predicting multiple energy sources simultaneously. Subsequently, employing the modeling mechanism of the grey prediction model, parameter estimates for the model are obtained. The differential equation set is solved using the discretization method to derive the model's time-response formula, ultimately yielding key modeling steps. To validate the model's effectiveness, the new model is applied to predict the consumption of natural gas, coal, and crude oil in China. Its validity is verified through three types of experiments: the first involves simulation and prediction for different modeling objects, the second effectively tests the model's robustness, and the third compares the new model with other classical grey models. These three types of experiments demonstrate that the new model can effectively capture the complex nonlinear relationships among various variables in the energy system, exhibiting unique stability and significant advantages, along with precise predictive capabilities. It provides robust data support for the planning, scheduling, and management of energy systems.