The plasmonic properties of gold nanostructures composed of a disk outside a nonconcentric ring are numerically studied by the finite difference time domain (FDTD) method. Simulated results show that two Fano resonances are formed as a result of the coupling of the octupolar and quadrupolar modes of the ring with the dipolar mode of the disk. The reduction in structural symmetry causes a red shift of the Fano resonances and distinct changes in spectral lineshape by offsetting the center of the inner surface of the ring to different directions. The effects of several geomet-ric parameters on the characteristics of Fano resonances are also discussed. In addition, the refractive index (RI) sensi-tivities for the two Fano resonances can be up to 581 nm/RIU and 780 nm/RIU with the corresponding figure of merits (FOMs) as large as 12.7 and 10.2, respectively. Such properties render the structures useful for potential applications in multi-wavelength sensors.