BRICS countries’ recent investments in technology have attracted attention, and they have become a part of the nations that conduct research around the world. The European Innovation Scoreboard (EIS), accepted as an effective benchmarking tool for technology policies, provides a comparative analysis of the innovation performances of many countries, including BRICS. In the current research, the innovation performances of BRICS countries were compared through EIS data, one of the most adopted benchmarking tools in technology policy discussions. Thus, it was aimed to determine the importance levels of the criteria used in the EIS data and to analyze the innovation processes of the countries in question. In this study, an integrated framework using CRiteria Importance Through Intercriteria Correlation (CRITIC) and Grey Relational Analysis (GRA) methods is presented to compare the innovation performances of BRICS countries. In the first stage of the application, the importance levels of the criteria are obtained using the CRITIC method, while in the second stage, countries are ranked according to their innovation performance through GRA. Data are obtained by compiling statistics from the EIS database created by the Commission of the European Communities. The results obtained in the practical application of the model rank the criteria according to their weights as follows: higher education (0.249), international joint publications (0.176), medium and high technology exports (0.122), frequently cited publications (0.113), PCT patents (0.094), public-private joint publications (0.085), designs (0.083) and trademarks (0.078). In addition, the BRICS countries are ranked according to their innovation performance as China (0.76), Russia (0.6), South Africa (0.516), Brazil (0.426), and India (0.378).