In this work, we have systematically investigated the spectra localized surface plasmon (LSPR) and the plasmonic resonance sensitivity of the silver nanoparticles (Ag-NPs) coated polyvinyl alcohol (PVA) by means of numerical study based on BHMie approximation with respect to the diameter of Ag-NPs, the thickness of PVA and the refractive index of medium variation. Lorentz-Lorentz approximation was used to calculate the refractive index of medium variation. The results showed that the LSPR spectra of Ag-NPs shifted to longer wavelength or red-shift as the diameter of Ag-NPs and the thickness of PVA increased. Then, we calculated the plasmonic resonance sensitivity from the spectra of Ag-NPs coated PVA by changing the refractive index of medium. Interestingly, the plasmonic resonance sensitivity of Ag-NPs coated PVA was exponentially decreased as the thickness of PVA increased. All results showed that the spectra of Ag-NPs was affected not only by the size of Ag-NPs and the thickness of PVA but also by the medium properties.