Many online platforms have deployed anti-fraud systems to detect and prevent fraudulent activities. However, there is usually a gap between the time that a user commits a fraudulent action and the time that the user is suspended by the platform. How to detect fraudsters in time is a challenging problem. Most of the existing approaches adopt classifiers to predict fraudsters given their activity sequences along time. The main drawback of classification models is that the prediction results between consecutive timestamps are often inconsistent. In this paper, we propose a survival analysis based fraud early detection model, SAFE, which maps dynamic user activities to survival probabilities that are guaranteed to be monotonically decreasing along time. SAFE adopts recurrent neural network (RNN) to handle user activity sequences and directly outputs hazard values at each timestamp, and then, survival probability derived from hazard values is deployed to achieve consistent predictions. Because we only observe the user suspended time instead of the fraudulent activity time in the training data, we revise the loss function of the regular survival model to achieve fraud early detection. Experimental results on two real world datasets demonstrate that SAFE outperforms both the survival analysis model and recurrent neural network model alone as well as state-of-theart fraud early detection approaches.