We proposed a new scoring system on software vulnerabilities, which calculates quantitatively the severity of software vulnerabilities. The proposed scoring system consists of metrics for vulnerability severity and scoring equations; the metrics are designed to measure the severity of a software vulnerability considering the prevalence of the vulnerability, the risk level of the vulnerability, the domestic market share of the software and the frequency of the software. We applied the proposed scoring system to domestically reported software vulnerabilities, and discussed the effectiveness of the scoring system, comparing it with CVSS and CWSS. We also suggested the prospective utilization areas of the proposed scoring system.