As one of many scientific and efficient risk assessment approaches, failure mode and effect analysis (FMEA) has been widely applied across various fields. There are two core issues in the FMEA approach: identifying the latent failure modes of the systems, products, processes and services and the risk assessment and the prioritization of those failure modes. Then, corrective measures must be taken in a timely and accessible manner to prevent the occurrence of failure modes with higher risk levels. In practice, several FMEA members from different fields are usually involved in the FMEA implementation process; the risk assessment information given by them may vary greatly. Therefore, it is necessary to integrate a consensus-building process into FMEA. Meanwhile, the psychological behaviours of FMEA members have had a great impact on the final prioritization of failure modes. Prospect theory is an effective approach for describing individual psychological behaviours. Therefore, this paper presents a novel linguistic FMEA approach to address the consensus issue from the perspective of prospect theory. In the proposed linguistic FMEA approach, a consensus measurement approach based on prospect theory is constructed. Then, a novel feedback adjustment mechanism is designed in which FMEA members can adjust not only their assessment information but also their reference points to achieve an acceptable consensus degree. Eventually, a practical application is used to show the validity and applicability of the proposed linguistic FMEA approach.