Crude oil, which is an important part of energy consumption, can drive or hinder economic development based on its production and consumption. Reasonable predictions of crude oil consumption in China are meaningful. In this paper, we study the grey‐extended SIGM model, which is directly estimated with differential equations. This model has high simulation and prediction accuracies and is one of the important models in grey theory. However, to achieve the desired modeling effect, the raw data must conform to a class ratio check. Unfortunately, the characteristics of the Chinese crude oil consumption data are not suitable for SIGM modeling. Therefore, in this paper, we use a least squares estimation to study the parametric operation properties of the SIGM model, and the gamma function is used to extend the integer order accumulation sequence to the fractional‐order accumulation generation sequence. The first‐order SIGM model is extended to the fractional‐order FSIGM model. According to the particle swarm optimization (PSO) mechanism and the properties of the gamma function of the fractional‐order cumulative generation operator, the optimal fractional‐order particle swarm optimization algorithm of the FSIGM model is obtained. Finally, the data concerning China’s crude oil consumption from 2002 to 2014 are used as experimental data. The results are better than those of the classical grey GM, DGM, and NDGM models as well as those of the grey‐extended SIGM model. At the same time, according to the FSIGM model, this paper predicts China’s crude oil consumption for 2015–2020.