Studying the development tendency of topics is an important part of the online social network (OSN) analysis. To solve the problems of ad hoc topic popularity, tendency prediction under insufficient samples, data sparsity and low accuracy of the prediction model, this study combines grey system theory with the neural network method to propose a new model for topic tendency prediction. In this study, the grey relational analysis method is used to construct the social network topic popularity evaluation index system, and the topic popularity tendency is classified and weighted based on the grey proximity, and then the integrated system combining GM(1,1) model with BP neural network (BP-NN) model is established. Taking Sina Weibo's bursty topic data as an example, the proposed model's effectiveness is verified. The experimental results show that the proposed hybrid methodology is better than a single independent prediction model and can be effectively used to predict the popularity of a social network topic.