System administrators and security officials of an organization need to deal with vulnerable IT assets, especially those with severe vulnerabilities, to minimize the risk of these vulnerabilities being exploited. The Common Vulnerability Scoring System (CVSS) can be used as a means to calculate the severity score of vulnerabilities, but it currently requires human operators to choose input values. A word-level Convolutional Neural Network (CNN) has been proposed to estimate the input parameters of CVSS and derive the severity score of vulnerability notes, but its accuracy needs to be improved further. In this paper, we propose a character-level CNN for estimating the severity scores. Experiments show that the proposed scheme outperforms conventional one in terms of accuracy and how errors occur.