Because ethylene-cracking furnace accounts for vast majority of energy consumption in ethylene production, energy-efficiency diagnosis of ethylene-cracking furnace is of great significance for improving energy utilization and production operation. In this paper, a two-level comprehensive energy-efficiency diagnosis problem is considered for both furnace level and internal chambers level. Apart from production load and feed composition, fault and exception operation also have influence on energy-efficiency, which leads to a multiple-working-condition energy-efficiency diagnosis problem under fault and exception operation. Therefore, this paper proposes a new energy-efficiency diagnosis scheme for ethylene-cracking furnace. Firstly, a two-level index system is designed to have an overall understanding of energy-efficiency of ethylene-cracking furnace and internal chambers. Secondly, fault and operation diagnosis criteria are established to identify fault samples, exception operation samples, and fault-and-exception-operation samples from inefficient samples after multi-working-condition classification. Thirdly, contributions of operation conditions, outputs, and internal chambers are quantified by step-by-step transformation and total differential methods to locate weak links in energy efficiency. Finally, effectiveness of diagnosis scheme is verified by applying it to a Chinese ethylene plant. Not only are three inefficient types detected, but also contributions of root causes resulting in inefficiency are quantified, which provides energy conservation and efficiency improvement suggestions for decision-makers.