Outbreak prediction in social networks is a part of popularity dynamic analysis of social networks, and it is an active research topic in the domain of social computing. This study proposes a social messages outbreak prediction model based on recurrent neural network (SMOP) by modeling the message propagation process. Compared with the traditional models on machine learning, SMOP directly models the arrival process of message without the need of tedious feature engineering in traditional methods. When it comes to point process models, SMOP is able to automatically learn the rate functions of propagation process, making it adaptable to a variety of scenarios. Moreover, time vector and user vector, which contain the periodicity of time and the user profile, are used as input to improve the performance of outbreak prediction. Experimental results on real word data sets such as Twitter and Sina Weibo show that SMOP has excellent data adaptability, and it is able to predict whether a message would outbreak with higher F1 score in the beginning of the message spread (within 0.5h).