In order to protect a software system from security attacks, it is important to remove the software security weaknesses through the entire life cycle of software development. To remove the software weaknesses more effectively, software weaknesses are prioritized and sorted continuously. In this paper, we introduce the existing scoring systems for software weakness and software vulnerability, and propose a new quantitative standard for the scoring system, which helps evaluate the importance of software weakness objectively. We also demonstrate the practicability of the proposed standard by scoring 2011 CWE/SANS Top 25 list with the proposed standard and comparing it to the original score of MITRE.