In the aspect of solving the problem of inefficiency of a complex information system of public finance management, the necessity of developing a methodology for system analysis and modeling of a complex information system (IS) is considered. Based on the synthesis of the provisions of systems theory, organization theory, decision theory and management theory, the main definitions of a separate theory, its axioms and the basic principles of evaluating the effectiveness of the system were proposed. The key feature of the management of the system is adaptation, the qualitative adjustment of which can enhance the beneficial effect of a complex system by developing a system-wide management strategy. The given conceptual descriptions of the adaptive management process indicate the need for continuous modeling of the system, the creation of models for managing the functioning and development of the complex IS as a complex ecosystem, where priority in decision-making should be focused on the synergetic effect of benchmarking, integration and centralization. Due to the expansion of scientific knowledge about the category of effectiveness of complex IS, the results of the study will further allow in practice to resolve some difficulties and contradictions in managing the development of a complex IS for public finance management.