The central aim of the article is company governance, i.e., researching governance of a company that does not want to be only financially successful but also direct its governance toward socially responsible governance. The article begins with the definition of “theoretical backgrounds,” in which social responsibility in regard to company governance improvement in quality is explained. The article then focuses on the measurement of the quality of company governance; in the research, the selected tool chosen to evaluate the governance of the chosen company regarding social responsibility, i.e., SEECGAN index, is used. Further, the case study of a Slovenian public limited liability company is used. One of the important research findings is the recognition that the addressed part of the SEECGAN index needs to be innovated and further developed. Additional questions for the completion of the index used presents the added value of the article. This article has two limitations: 1) it focuses only on the tool chosen to evaluate the governance of the chosen company regarding social responsibility; 2) the case study is based on publicly accessible data.