One of the most common models of national innovation systems as of today is the triple helix model. Four- and five-tier constructions also exist and present an option for adapting the triple helix model to the economic conditions of different countries. In this paper, we are based on the system economic theory and propose to consider the national innovation system (NIS) of Russia as a complex of four socio-economic macro-subsystems: science, government, education, and business. In this case, science acts as a system of the object type: the government – as the environment type, education – as the process type, and business – as the project type. The interaction order and role functions of these subsystems are determined. A quantitative evaluation of the quadruple helix subsystem parity was carried out; namely, the system balance indices of the NIS of Russia for 2015–2019 were calculated. The world countries’ data used to calculate the global innovation index according to the methodology of the WIPO constitute the statistical basis for the calculation. The place of the NIS of Russia among the national innovation systems of other countries for 2019, according to two parameters: the NIS subsystems balance and the effectiveness of NIS activities, was determined. For comparison, 16 countries, divided into four groups, were selected: innovative leaders, catching-up countries, lagging countries, and outsiders. It is established that Russia belongs to the countries of the second group. It is shown that to harmonize the NIS of Russia, to increase its efficiency and move Russia to the group of leaders, it is necessary to revise the economic policy and add to it, along with increasing the efficiency of innovative activity, another goal such as improving the balance of the quadruple helix subsystems.