Quantitative risk assessment is a crucial step in the safety analysis of process systems. The advancement of modern process systems has made a large volume of process data and information available for process safety analysis. This tendency urges the need for developing new risk assessment approaches. Fault tree (FT), a conventional risk analysis method, is found to be ineffective in dynamic risk analysis and data analytics due to its static nature and reliance on experts' judgment. Artificial Neural Network (ANN) is a structured model built upon data samples and learning algorithms to process complex input/output data in the way that it is being trained. The application of ANN can help to overcome some of the limitations of FT. The data-driven nature, independency on prior information on events relationships, and less reliance on experts’ judgment are the advantages of ANN over FT. The use of ANN in risk assessment is not a new concept. However, there is limited work on the development of ANN-based risk assessment models using conventional methods such as FT as an informative base. This study proposes a methodology for mapping FT into ANN to support the convenient and practical application of ANN in risk assessment. The proposed method is demonstrated through its application to the analysis of a system failure in the Tesoro Anacortes Refinery accident. The results have shown that the ANN model mapped from the FT is an effective risk assessment technique.