We consider a two-stage parallel-series system having three sub-systems. The independent two sub-systems of the first stage are linked in parallel and then linked to the third sub-system of the second stage in series. The deterministic two-stage parallel-series system approach is extended to uncertain/imprecise environment where the data are represented as fuzzy numbers. Using the Zadeh extension principle, we develop a fuzzy two-stage parallel-series system to determine the lower and upper bound fuzzy efficiencies of the decision-making units with the help of α- cut and rank the DMUs using the ranking index approach. The proposed methodology is illustrated using the case of Taiwan’s non-life insurance companies. © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.