Metal nanoparticles have potential applications in the fields of optical sensing and optoelectronic devices, due to the localized surface plasmon resonance (LSPR) which enhances the spontaneous emission rate of nearby fluorescent molecules. The LSPR of metal nanoparticles is closely related to its material, shape, size and ambient medium, which affects the applications of nanoparticles in specific devices. In this paper, the LSPR effect of silver nanoparticles (SNPs) with different shapes of sphere, ellipsoid, cube, and triangular-prism, is investigated by using a three-dimensional finite difference time domain. The absorption and scattering spectra of the individual SNPs are first calculated. The resonance peaks are red shifted and enhanced with sharpness increasing from the nano-sphere to the nano-triangular-prism because the surface charges accumulate in the sharp corners. Then the effects of SNPs on the radiation power of the dipole source and light extraction efficiency of the light-emitting diodes (LEDs) are studied. The dipole radiation power decreases near the resonance wavelength due to the absorptions of SNPs, while increases after the resonance wavelength because of the coupling between the SNP LSPR and the dipole radiation. The calculated electric field distribution shows that the LSPR electric field of the SNPs concentrate near the surface of the dielectric film because of the interaction between the SNPs and the film. The concentrated electric field helps to improve the coupling between the LSPR and the dipole, which enhances the dipole radiation power in the LED. In the several kinds of SNPs, nano-cube SNP shows the most significant improvement on the dipole radiation power because of the strongest interaction with the dielectric film. In addition, the scattering effect of the SNP reduces the internal total reflection of light and improves the light extraction efficiency of the LED. Nano-ellipsoid SNP significantly enhances the light extraction because of its strongest scattering intensity. Further, the influence of the refractive index of the dielectric film on the dipole radiation power is studied. It is found that a higher refractive index of dielectric film helps to enhance the interaction between the SNPs and the film and improves the dipole radiation power. The optimized value of refractive index is acquired through detailed calculation.