In this article, a new systemic risk assessment approach, which combines failure mode and effect analysis (FMEA) and pessimistic–optimistic fuzzy information axiom (POFIA) considering acceptable risk coefficient (ARC), is proposed to evaluate the risk of railway dangerous goods transportation system (RDNGTS). This approach transforms the system risk assessment problem into the rank problem of severity of risk factors affecting system security. The triangular fuzzy numbers (TFNs) are applied to score the severity of failures (S), portability of occurrence (O), and possibility of detection (D) for each RDNGTS risk subindicator. The information contents of S, O, and D are calculated for each risk subindicator, two models are applied to calculate the information contents: POFIA, and POFIA considering ARC (POFIA-ARC). The product of information contents of S, O, and D is used to replace the risk priority number of FMEA. entropy weight method is used to calculate the weight of each risk subindicator. The comparison among the FMEA-POFIA-ARC, FMEA-POFIA, FMEA, FMEA with TFNs is conducted based on the historical data of Chinese RDNGTS accidents from 1986 to 2017. Results show that the potential human risk should be paid more attention. Compared with the analysis results of statistical accident number, the results of the approaches proposed in this article (especially the FMEA-POFIA-ARC) are more reliable than the results of FMEA and FMEA TFNs combined approach.