In this work, we compared and analyzed the optical properties and surface plasmon resonant effects on solid gold nanorod and gold-shell nanorod by using three-dimensional finite element method. Scattering cross sections (SCSs), electric amplitude and standing wave have been investigated under four different size and different polarization (i.e., x- and y- polarization) states. Simulation results can be used for field enhancement spectroscopy and related applications in nanophotonics devices.