An Ag/SiO₂/Ag sandwich delta nanostar with three sharp angles (30°) is proposed. The extinction efficiency property with a variation in environment refractive index has been investigated in detail by the finite difference time domain method. The refractive index response sensitivity is 482.67 nm/RIU. And the correlations between resonance wavelengths and thickness of the dielectric layer are also established. It reveals that as the thickness increases, the peak wavelength turns to red shift, and a tunable resonance wavelength is achieved through the thickness adjusting of the SiO₂ layer. The maximum of the electric field enhancement is 833.776 with the thickness of the dielectric layer h=40 nm. Moreover, the influence of the vertex truncation on the extinction spectra and the refractive index sensitivity has also been analyzed.