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A finite element model was built to investigate how to optimize localized plasmon resonances of an Ag-coated dielectric tip for tip-enhanced Raman spectroscopy (TERS). The relation between the resonance frequency, the electric field enhancement and the optical constant of the dielectric tip was numerically investigated. The results show that increasing the refractive index of the dielectric tip can significantly red shift the localized plasmon modes excited on the Ag-coated dielectric tip, and consequently alter the field enhancement. Moreover, the influence of the width of the resonance on the Raman enhancement was also considered. When taking all the factors into account, we find that an Ag-coated low-refractive index dielectric tip provides the best Raman enhancement in the blue—green spectral range. This is consistent with our prior experimental results.