The accurate prediction of China’s energy consumption and CO2 emissions is important for the formulation of energy and environmental policies and achieving carbon neutrality. This paper proposes a new weighted error evaluation criterion that emphasizes the importance of new data, thereby enabling more accurate capture of the variation characteristics of new data and reflecting the principle of new information priority. By optimizing the development coefficient, grey action, and parameters in the time response formula of the traditional GM(1,1), a novel optimized model, OGMW(1,1), is constructed. The accuracy of the new model is verified by three cases from the literature. The future trends of primary energy, oil, and coal consumption and CO2 emissions in China are predicted over the next five years. The conclusions are as follows: First, the new weighted error evaluation criteria are effective and reasonable and can indicate whether a grey model can reliably use the most recent information for modeling. Second, based on the new error evaluation criteria, the development coefficient, ash action, and parameter C in the time response function can be optimized. The results show that the optimization method is reasonable. Third, compared with the traditional models GM, GMO, and ARIMA, the OGMW(1,1) provides better simulation and prediction accuracy, and new information can be prioritized more effectively. Fourth, the forecasting results indicate that China will increase its consumption of primary energy, oil, and coal, as well as its CO2 emissions. Notably, the growth rates of primary energy and oil consumption are high at approximately 22.7% and 25%, coal consumption will increase slightly, and CO2 emissions will increase by approximately 11%.