The dramatic increase of the aging population is a current and primary livelihood issue in China. It is very important to accurately predict the aging population for policy-makers such as governments and insurance companies. To explore the future development trend of China’s aging population, a novel grey prediction FPTGM(1,1,α) model is established in this paper. The data from 2003 to 2012 are used to build the model, and the data from 2013 to 2018 are used to assess the modelling accuracy. The results show that the fitting and forecasting accuracy of the proposed FPTGM(1,1,α) model are higher than those of other models. This indicates that the novel grey model is more suitable for predicting the aging population in China. Combined with the idea of metabolism, the FPTGM(1,1,α) model is applied to predict China’s aging population from 2019 to 2042. Finally, some reasonable suggestions for dealing with the aging population are put forward to the government and other decision-makers.