FPSO production process is prone to leakage, and failure to respond promptly and effectively will lead to accident escalation and serious consequences. However, traditional safety assessment methods cannot handle the nonlinear relationships between human, technology, and organization in emergency response process. This study proposes a quantitative FRAM to evaluate the emergency response resilience of FPSO leakage. This method establishes a resilience evaluation framework including three tiers: function, ability, and system, which can quantify system resilience based on the variability of function. First, identify basic functions according to the four stages of monitoring, response, learning and anticipation in the emergency response process, and establish the FRAM model of FPSO leakage emergency response. Then, the quantitative FRAM and Monte Carlo simulation are combined to calculate the variabilities of functions under different operating conditions. Finally, based on the simulation results, the variabilities of basic functions are aggregated and statistically analyzed to quantify system resilience. The implementation process of this method is illustrated by a case study. The influence of different factors on the system resilience is analyzed by setting various operation scenarios, and critical functions are identified by sensitivity analysis, which can provide reference for improving system resilience and ensuring FPSO safety production.