Power distribution systems are vulnerable to natural disasters and malicious attacks. An efficient and accurate online risk assessment tool is very necessary to provide timely warning information for emergency dispatch of resilient distribution systems. However, conventional analytical risk assessment methods are subject to known network information, while emerging data-driven methods rarely incorporate resilient resources into the risk assessment procedures, limiting their accuracies when applied to extreme events. To solve the problems, this paper proposes an improved online data-driven risk assessment method adaptive for resilient distribution systems. Twenty-five basic operational indexes from practical experience are chosen to indirectly reflect the system risk, and the complicated relationship between the indexes and risk is characterized by entropy weights and gray correlation degrees. The proposed method is validated on a modified 33-node system, and the results show that it has better accuracy compared with similar approaches in online risk assessment during extreme events. The whole scheme can be helpful for the software design and hardware layout of future resilient distribution systems.