Efficiency scores for the national innovation systems (NISs) in 22 countries including the BRICS and the G7 are calculated using data envelopment analysis (DEA). Factors that may affect the efficiency of the NIS are summarized based on the NIS approach and the new growth theory. Empirical evidence is provided using panel data analysis and principal component analysis. The results of the efficiency calculations and the empirical tests show the following. (1) The BRICS differ greatly in the efficiency of their NISs, with China, India, and Russia ranking fairly high, and Brazil and South Africa ranking low. (2) In accordance with the NIS approach and the new growth theory, there are many factors that affect the NISs including ICT infrastructure, enterprise R&D, market environment, governance, education systems, economic scale, natural endowments, and external dependence. (3) Enterprise innovation is of particular importance for the NISs. To improve the efficiency of innovation systems, efforts should be made to improve the market conditions, governance, and financial structures, and create a sound environment for R&D. (4) ICT infrastructure, economic scale, and openness affect the diffusion of knowledge and technology, and in turn affect NIS efficiency. (5) The BRICS have low governance levels and a high dependency on natural resources, both of which are determined by their stage of development and extensive growth patterns. To avoid the so-called middle-income trap, the BRICS should transform their factor-driven growth patterns into innovation-driven growth patterns. China still needs to improve its ICT infrastructure, its governance systems, and its education system. During its 12th five-year plan, more effort should be devoted to these fields and to improving external conditions for R&D.