A novel approach for measuring the nonlinear refractive index of an optical fiber utlizing the bistable behavior of the double coupling optical fiber ring resonator was proposed and investigated. The switch-off or switch-on power decreases with an increase in the nonlinear refractive index n2 (m2/W), and the dependence of swith-off or switch-on power on the nonlinear refractive index was analyzed numerically. Simulation results showed that the switch-off power and switch-on power (in dBW) decreased linearly with 102log()n in a 100-m-length fiber ring resonator, when n2 changed from 3.2×10-20 m2/W to 2.5×10-17 m2/W or nearly n2=3.2×10-20 m2/W. These mean that high accuracy as well as large-scale nonlinear refractive index measurement can be achieved by the proposed approach.