The energy demand in developed and developing nations is steadily increasing with Liquefied Natural Gas (LNG) being a prominent source of energy to meet the growing demand. However, the social acceptance of LNG facilities largely depends on the successful implementation of appropriate safety standards and risk management programs. Therefore, it is vital to continue to improve existing risk assessment strategies to deal with the safety concerns of these facilities. FMECA (Failure Mode Effects and Criticality Analysis) approach is very effective in identifying failure modes and prioritising them by developing a Risk Priority Number (RPN). Several literature have discussed the difficulty in prioritization of failure modes having identical RPN values. This paper presents the application of Fuzzy based FMECA approach to an LNG unloading facility in an LNG terminal located in south India. This fuzzy based FMECA approach uses Fuzzy RPN values which reduces the difficulties in prioritization of failure modes of critical failures. The effectiveness of this approach is demonstrated by applying it to an operational LNG unloading facility in one of the major LNG terminals. The successful identification and ranking of critical failure modes in LNG unloading facility is to be very useful for LNG industries to prioritize their corrective and preventive actions, thereby improving their safety standards.