An analytical solution is developed to describe the localized surface plasmon resonance (LSPR) responses to complicated environmental refractive index of metal nanostructures with arbitrary shapes. Both local and bulk refractive index sensitivity equations with their essential influence parameters are also presented. Theoretical analysis and numerical calculation results demonstrate that the peak wavelength of the LSPR spectra for metal nanostructures increases exponentially as the analyte thickness grows, and is greatly dependent on the refractive index of analyte, receptor thickness as well as metal nanostructures shapes and materials. The bigger the refractive index of analyte, the greater the spectra response. Furthermore, a thicker receptor will induce poorer local refractive index sensitivity and a sharper shape will bring on greater bulk refractive index sensitivity. These results can be used as guidelines in fabricating high sensitive LSPR-based biochemical sensors.