It is increasingly necessary to perform risk analysis in marine structures, to ensure system safety, as they are large and complex. In view of the shortcomings of failure mode and effect analysis (FMEA), a modified fuzzy TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) approach is proposed that is based on fuzzy evidence reasoning (FER), and considers the risk factor rating and relative weight. The presented method is used to prioritize the risk of equipment failure modes for the floating production storage and offloading system (FPSO) oil and gas processing system. The subjective weights and objective weights of occurrence (O), severity (S), and detectability (D) have been considered comprehensively. The subjective experience of the experts and the objective information reflected by the O, S, and D ratings are all included in the weights, making the ranking results closer to reality. The results can be scientific references for decision-makers in risk identification.