The trend of big data implies novel opportunities and challenges for improving supply chain management. In particular, supply chain risk management can largely benefit from big data technologies and analytic methods for collecting, analyzing, and monitoring both supply chain internal data and environmental data. Due to the increasing complexity, particular attention must not only be put on the processing and analysis of data, but also on the interaction between big data information systems and users. In this paper, we analyze the role of big data in supply chains and present a novel framework of a supply chain risk management system for improving supply chain planning and supply chain risk management under stochastic environments by using big data technologies and analytics. The process-oriented framework serves as a guideline to integrate and analyze big data as well as to implement a respective supply chain risk management system. As such, this paper provides a novel direction of utilizing big data in supply chain risk management.