At present, the energy structure of China is shifting towards cleaner and lower amounts of carbon fuel, driven by environmental needs and technological advances. Nuclear energy, which is one of the major low-carbon resources, plays a key role in China's clean energy development. To formulate appropriate energy policies, it is necessary to conduct reliable forecasts. This paper discusses the nuclear energy consumption of China by means of a novel fractional grey model FAGMO(1,1,k). The fractional accumulated generating matrix is introduced to analyse the fractional grey model properties. Thereafter, the modelling procedures of the FAGMO(1,1,k) are presented in detail, along with the transforms of its optimal parameters. A stochastic testing scheme is provided to validate the accuracy and properties of the optimal parameters of the FAGMO(1,1,k). Finally, this model is used to forecast China's nuclear energy consumption and the results demonstrate that the FAGMO(1,1,k) model provides accurate prediction, outperforming other grey models. (C) 2018 Elsevier Ltd. All rights reserved.