The technical applications that will ensure that the software system continues to work correctly against malicious attacks is called software security. Weaknesses and flaws in the software system that cause the risk of being hacked are defined as software vulnerability. Software vulnerabilities can cause serious damage by compromising the confidentiality, integrity, usability and accessibility of a software. If software vulnerabilities are detected at an early stage and managed effectively, the risk of system attack and damage can be reduced. Artificial intelligence-based methods have been used in recent years to automatically manage software security vulnerabilities. In this study, a deep learning-based automatic classification method has been proposed to help identify and manage the categories of security vulnerabilities. The developed method is built on the convolutional neural network (CNN) model, which is one of the deep neural network models. The National Vulnerability Database (NVD) was used to measure the performance of the proposed model. The CNN model used in the study has been shown to provide high performance in automatic classification of software security vulnerabilities.