Quantifiable predictability in the citation counts of articles is significant in scientometrics and informetrics. Many metrics based on the citation counts can evaluate the scientific impact of research articles and journals. Utilising time series models, an article’s citation counts up to the yth year after publication can be predicted by those up to the previous years. However, the typically used models cannot predict the fat tail of the actual citation distributions. Thus, based on cumulative advantage of the citation behaviour, we propose a method to predict the accumulated citation counts, by using a random number sampled from a power-law distribution to modify the results given by a recurrent neural network (RNN), long short-term memory. Extensive experiments on the data set including 17 journals in information science verified the effectiveness of our method by the good fittings on distributions and evolutionary trends of the citation counts of articles. Our method has the potential to be extended to predict other popular assessment measures such as impact factor and h-index for journals.