The Common Vulnerabilities and Exposures (CVE) represent standard means for sharing publicly known information security vulnerabilities. One or more CVEs are grouped into the Common Weakness Enumeration (CWE) classes for the purpose of understanding the software or configuration flaws and potential impacts enabled by these vulnerabilities and identifying means to detect or prevent exploitation. As the CVE-to-CWE classification is mostly performed manually by domain experts, thousands of critical and new CVEs remain unclassified, yet they are unpatchable. This significantly limits the utility of CVEs and slows down proactive threat mitigation. This paper presents the first automatic tool to classify CVEs to CWEs. ThreatZoom uses a novel learning algorithm that employs an adaptive hierarchical neural network which adjusts its weights based on text analytic scores and classification errors. It automatically estimates the CWE classes corresponding to a CVE instance using both statistical and semantic features extracted from the description of a CVE. This tool is rigorously tested by various datasets provided by MITRE and the National Vulnerability Database (NVD). The accuracy of classifying CVE instances to their correct CWE classes are 92% (fine-grain) and 94% (coarse-grain) for NVD dataset, and 75% (fine-grain) and 90% (coarse-grain) for MITRE dataset, despite the small corpus.