In this paper,we simulate Localized Surface Plasmon Resonance(LSPR) absorption of periodic Au nano-ring arrays and single Au nanoparticles using the Finite Difference Time Domain (FDTD) method.We choose input plane waves of different wavelengths and discuss the relation between the absorption peak of the Au array and the variable external dielectric constants.It is found that the sensitivity of these sensors based on LSPR is improved compared to the common sensors and the enhancement is caused by the periodical structure.We also investigate the spectrum characteristic of a single Au nanoparticle and discuss the relation between the absorption peak and the size of the nanoparticle.