GM(1,1) is mainly used for monotone sequence prediction. But when used for sequences with peaks, such as the total population, total energy consumption, etc, GM(1,1) is not a good consideration. This paper proposes a peak prediction algorithm based on the model GM(1,1) (GPPA) to forecast the development trend of the system in the long run. According to the developing law of the system, the growth inflection point is analyzed and determined, and from which the growth rate of the system will be smaller and its trend can be decomposed into two parts based on the logistic curve of population growth: one is the original growth trend and the other one is the restraining trend of the retarding factors. Metabolic GM(1,1) is used to model both the two trends respectively and get the predictions of them. The difference between the predictions is used to forecast the development of the system. In addition, the energy consumption and population are taken as examples to prove the applicability of the method.