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Research on energy-saving retrofits of the existing industrial systems can effectively improve the systems' energy-saving level and increase company revenue. The energy-saving bottleneck diagnosis for systems is the foundation of the energy-saving retrofit design. The diagnosis also aims to yield a more targeted energy-saving retrofit, thus ensuring the energy-saving effect and investment income of the transformation project. Therefore, this paper proposes a new method to diagnose the energy-saving bottleneck of the existing industrial systems. First, the energy-saving bottleneck diagnosis is decomposed into two parts: the diagnosis of energy-saving bottleneck units and the diagnosis of energy-saving bottleneck factors. Then, the energy density decomposition method is improved and a multi-mode energy efficiency density decomposition method is proposed. Next, an energy-saving bottleneck diagnosis method for industrial systems based on multi-mode energy efficiency density decomposition and an orthogonal test method is proposed. The proposed method can analyze the energy-saving potential of existing systems, accurately locate energy-saving bottlenecks, and avoid the dependence on a large amount of expert experience or complete production data in the existing methods. Finally, the proposed method is applied to an actual circulating cooling water system and the system energy-saving bottleneck diagnosis is realized, thus verifying the practicability of the method. • Energy-saving bottlenecks in industrial systems are analyzed and decomposed. • A method for energy-saving bottleneck diagnosis from two directions is proposed. • An improved energy efficiency density decomposition method is proposed. • The diagnosis of energy-saving bottlenecks in industrial systems is achieved. • The verification is performed for an industrial circulating cooling water system. [ABSTRACT FROM AUTHOR]