Recent regulatory requirements for shipping emissions control have led to the adoption of Liquefied Natural Gas (LNG) as a marine fuel and the design of LNG-fuelled vessels. Considering the potential safety implications due to system failure/unavailability, this study aims at the safety analysis of a low-pressure LNG fuel feeding system using a novel model-based methodology. The proposed methodology is based on the functional system modelling, leading to the failure diagrams development, and combines the use of Failure Modes, Effects, and Criticality Analysis (FMECA) and Fault Tree Analysis (FTA), which are performed in MADe™ and PTC Windchill software environments. The FMECA results are employed to identify the investigated system critical components and failures as well as specifying the top events for the subsequently performed FTA, which evaluates the top events failure rates. The system critical components identification leads to the system design modification targeting reduced safety metrics. This study results demonstrate that the evaporator, pressure build-up unit, sensors, and cryogenic valve assemblies are the most critical components of the investigated system, whilst the enhanced system design exhibits a failure rate reduced by 69% in comparison to the baseline system. This study reveals the advantages of the developed methodology along with some limitations of the employed tools and contributes to the quantitative safety analysis and design of ship complex systems.