Accurately forecasting energy demand can better predict future changes in energy demand. This study is aimed to develop more accurate clean energy prediction model from two perspectives of the modeling mechanisms and improvements on the model structure. For this purpose, a novel Riccati–Bernoulli differential equation is established through social practice theory, supply–demand relationship, and the preference of consumption in the energy economy. Considering the limited information in observation data, this differential equation is then transformed into a grey Riccati–Bernoulli model (GRBM(1,1)) according to the differential information principle. With the response function solved on the basis of polynomial equation theory and the power exponent optimized combining the modified flower pollination algorithm, the main process of GRBM(1,1) can be summarized. The four validation examples are provided for confirming the effectiveness and reliability of the new model by comparing with other existing models. Finally, the proposed model is employed to estimate and forecast the clean energy consumption in China and India. The results show that the proposed model demonstrates better estimation in all cases and efficiency in short-term clean energy consumption forecasting. Therefore, by using this optimum model, China’s preference coefficient in total energy consumption is 0.7103, lower than that of India (0.8799), and China’s preference coefficient in clean energy consumption is 0.9665, higher than that of Indian (0.7155), which means China has less interest to increase total energy consumption but more interest in popularizing the clean energy.