Predicting the scope of a message accurately in social networks is an important part of public opinion analysis, which has received extensive attention in the field of data mining. Most of the current research mainly uses social network topology and user action logs to predict the spread of social messages. It is usually easy to obtain action log about users in real applications, but the topology of the social network (for example, the friend relationship between users) is not easy to obtain. Therefore, non-topology social message prediction has good prospects for broader applications. In this paper, we propose a new method called NT-EP for predicting the propagation scope of social messages. NT-EP consists of four parts: 1)We construct a weighted propagation graph for each message based on the characteristics of message propagation decay over time, and then use a random walk strategy to obtain multiple propagation paths on the propagation graph; 2)We put multiple propagation paths of the target message into Bi-GRU, and combine the attention mechanism to obtain the propagation feature representation for the target message; 3)We use the gradient descent method to calculate the influence representation about other messages; 4)Combining the propagation feature representation for the target message with the influence representation about other events, we predict the propagation scope of the target message. The experimental results on Sina microblog and Flixster dataset show that our method is superior to existing social event prediction methods in terms of many indicators such as MSE and F1-score.