Chemical event evolutionary graph (CEEG) is an effective tool to perform safety analysis, early warning, and emergency disposal for chemical accidents. However, it is a complicated work to find causality among events in a CEEG. This paper presents a method to accurately extract event causality by using a neural network and structural analysis. First, we identify the events and their component elements from fault trees by natural language processing technology. Then, causality in accident events is divided into explicit causality and implicit causality. Explicit causality is obtained by analyzing the hierarchical structure relations of event nodes and the semantics of component logic gates in fault trees. By integrating internal structural features of events and semantic features of event sentences, we extract implicit causality by utilizing a bidirectional gated recurrent unit (BiGRU) neural network. An algorithm, named CEFTAR, is presented to extract causality for safety events in chemical accidents from fault trees and accident reports. Compared with the existing methods, experimental results show that our method has a higher accuracy and recall rate in extracting causality.