By deviating the nanodisk from the center in the silver nanocrescent/nanodisk structure, we find that the dipole, quadrupole and octupole modes can all induce very high local electric field enhancement (LFE, more than 750) for the coupling of nanocrescent and crescent gap modes, which makes the resonant wavelengths of the non-concentric nanostructures change from the visible to near infrared regions. In addition, the LFE factor of the quadrupole mode is more than 1000, which is suitable for single molecular detection by local surface enhanced spectroscopy.